Structures and methods for reducing aberration in optical systems

ABSTRACT

An optical system includes multiple cubic crystalline optical elements and one or more polarization rotators in which the crystal lattices of the cubic crystalline optical elements are oriented with respect to each other to reduce the effects of intrinsic birefringence and produce a system with reduced retardance. The optical system may be a refractive or catadioptric system having a high numerical aperture and using light with a wavelength at or below 248 nanometers. The net retardance of the system is less than the sum of the retardance contributions of the respective optical elements. In one embodiment, all cubic crystalline optical elements are oriented with identical three dimensional cubic crystalline lattice directions, a 90° polarization rotator divides the system into front and rear groups such that the net retardance of the front group is balanced by the net retardance of the rear group. The optical system may be used in a photolithography tool to pattern substrates such as semiconductor substrates and thereby produce semiconductor devices.

PRIORITY APPLICATION

This application is a divisional of U.S. Non-Provisional patentapplication Ser. No. 10/178,601, filed Jun. 20, 2002, which claims thebenefit of priority under 35 U.S.C. §119(e) to U.S. Provisional PatentApplication No. 60/385,427, filed May 31, 2002 and entitled “Structuresand Methods for Reducing Aberrations in Optical Systems”, U.S.Provisional Patent Application No. 60/367,911, filed Mar. 26, 2002 andentitled “Structure and Method for Improving Optical Systems”, U.S.Provisional Patent Application No. 60/363,808, filed Mar. 12, 2002, andentitled “Correction of Intrinsic Birefringence Using Rotators”, U.S.Provisional Patent Application No. 60/332,183, filed Nov. 21, 2001, andentitled “Compensation for Intrinsic Birefringence Effects in CubicCrystalline Optical Systems” as well as U.S. Provisional PatentApplication No. 60/335,093, filed Oct. 30, 2001, and entitled “IntrinsicBirefringence Compensation”, each of the foregoing applications ishereby incorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to reducing aberration in optical systems.More particularly, the present invention relates to an apparatus andmethod for reducing polarization aberrations in optical systems such aslithographic imaging systems comprising cubic crystalline opticalelements having intrinsic birefringence.

2. Description of the Related Art

In order to increase levels of device integration for integrated circuitand other semiconductor components, device features having smaller andsmaller dimensions are desired. In today's rapidly advancingsemiconductor manufacturing industry, the drive is to produce suchreduced device features in a reliable and repeatable manner.

Optical lithography systems are commonly used to form images of device,patterns upon semiconductor substrates in the fabrication process. Theresolving power of such systems is proportional to the exposurewavelength; therefore, it is advantageous to use exposure wavelengthsthat are as short as possible. For sub-micron lithography, deepultraviolet light having a wavelength of 248 nanometers or shorter iscommonly used. Wavelengths of interest include 193 and 157 nanometers.

At ultraviolet or deep ultraviolet wavelengths, the choice of materialsused to form the lenses, windows, and other optical elements of thelithography system is significant. Such optical elements preferably aresubstantially optically transmissive at short wavelengths used in theselithography systems.

Calcium fluoride and other cubic crystalline materials such as bariumfluoride, lithium fluoride, and strontium fluoride, represent some ofthe materials being developed for use as optical elements for 157nanometer lithography, for example. These single crystal fluoridematerials have a desirably high transmittance compared to ordinaryoptical glass and can be produced with good homogeneity.

Accordingly, such cubic crystalline materials are useful as opticalelements in short wavelength optical systems including but not limitedto wafer steppers and other projection printers used to produce smallfeatures on substrates such as semiconductor wafers and other substratesused in the semiconductor manufacturing industry. In particular, calciumfluoride finds particular advantage in that it is an easily obtainedcubic crystalline material and large high purity single crystals can begrown. These crystals, however, are expensive, and certain orientations,such as the <100> and <110> crytallographic orientations are moreexpensive than others, like the <111> crystal orientation.

A primary concern regarding the use of cubic crystalline materials foroptical elements in deep ultraviolet lithography systems is anisotropyof refractive index inherent in cubic crystalline materials; this effectis referred to as “intrinsic birefringence.” For light propagatingthrough a birefringent material, the refractive index varies as afunction of polarization and orientation of the material with respect tothe propagation direction and the polarization. Accordingly, differentpolarization components propagate at different phase velocities andundergo different phase shifts upon passing through an optical elementcomprising birefringent material.

When used for construction of elements of an optical system, thebirefringent properties of these cubic crystalline materials may producewavefront aberrations that significantly degrade image resolution andintroduce field distortion. These aberrations are particularlychallenging for optical instruments employed in photolithography intoday's semiconductor manufacturing industry where high resolution andtight overlay requirements are demanded by an emphasis on increasedlevels of integration and reduced feature sizes.

It has been recently reported [J. Burnett, Z. H. Levine, and E. Shipley,“Intrinsic Birefringence in 157 nm materials,” Proc. 2^(nd) Intl. Symp.on 157 nm Lithography, Austin, Intl. SEMATECH, ed. R. Harbison, 2001]that cubic crystalline materials such as calcium fluoride, exhibitintrinsic birefringence that scales as the inverse of the square of thewavelength of light used in the optical system. The magnitude of thisbirefringence becomes especially significant when the optical wavelengthis decreased below 250 nanometers and particularly as it approaches 100nanometers. Of particular interest is the effect of intrinsicbirefringence at the wavelength of 157 nanometers (nm), the wavelengthof light produced by an F₂ excimer laser, which is favored in thesemiconductor manufacturing industry. Strong intrinsic birefringence atthis wavelength has the unfortunate effect of producing wavefrontaberrations that can significantly degrade image resolution andintroduce distortion of the image field, particularly for sub-micronprojection lithography in semiconductor manufacturing.

Thus, there is a need to reduce these wavefront aberrations caused byintrinsic birefringence, which can degrade image resolution and causeimage field distortion. Such correction is particularly desirable inprojection lithography systems comprising cubic crystalline opticalelements using light having wavelengths in the deep ultraviolet range.

SUMMARY OF THE INVENTION

One aspect of the invention comprises an optical apparatus having anoutput. This optical apparatus comprises one or more optical elementswith polarization aberrations that alter the output of the apparatus.The optical apparatus further comprises polarization transformationoptics, e.g., polarization rotation optics, configured to reduce thecontributions of the polarization aberrations to the output.

Another aspect of the invention comprises an optical system comprisingat least one cubic crystalline optical element aligned along an opticalaxis and polarization rotation optics inserted along this optical axis.The at least one cubic crystalline optical element is birefringent andimparts retardance on a beam of light propagating through the opticalsystem along the optical axis. The polarization rotation optics rotatesthe polarization of the beam of light to reduce the retardance.

In another aspect of the invention, an optical apparatus having anoutput comprises a plurality of optical elements divided into first andsecond sections and polarization conversion optics disposed between thefirst and second optical sections. The first and second sections haveassociated therewith polarization aberrations originating from variationin optical properties of the respective sections with polarization. Thepolarization aberrations affect the output of the optical apparatus. Thepolarization aberrations associated with the first section aresubstantially similar to the polarization aberrations associated withthe second section. The polarization conversion optics are configured totransform an input polarization into a orthogonal output polarizationsuch that the polarization aberrations associated with the first sectionat least partially offset the polarization aberrations associated withthe second section. The effects of polarization aberrations on theoutput of the optical system are thereby reduced.

Another aspect of the invention comprises an optical imaging system forproducing an optical image. This optical imaging system includes one ormore powered optical elements with polarization aberration that degradesthe optical image. The optical imaging system further comprises apolarization rotation system configured to reduce the contributions ofthe polarization aberration to the degradation of the optical image.

Still another aspect of the invention comprises an optical apparatus fortransmitting a light. This optical apparatus comprises a plurality ofoptical elements having birefringence that introduces retardance to thelight and a circular retarder having orthogonal circulareigenpolarization states. The circular retarder produces phase delaybetween the eigenpolarization states substantially equivalent to an oddnumber of quarter wavelengths of the light.

In yet another aspect of the invention, an optical system includes afirst optics section for receiving a beam of light having a polarizationthat is propagating therethrough and a second optics section outputtingsaid beam of light. The first and second optics sections introduce phasedelay between orthogonal polarization states of the beam of light. Theoptical system further includes means for rotating the polarization ofthe beam to reduce total phase delay between the polarization states ofthe beam of light output from the optical system.

Another aspect of the invention comprises a method of optically imaging.In this method, light is collected from an object using at least oneoptical element which introduces first polarization aberrations. Thepolarization of the light is rotated. The light collected is propagatedthrough at least one element thereby introducing second polarizationaberrations which at least partially cancel the first polarizationaberrations.

In another aspect of the invention, a method includes propagating lighthaving first and second orthogonal polarization components through afirst optics section having first and second eigenpolarization states.The first polarization component is converted into the secondpolarization component and the second polarization component isconverted into the first polarization component. After performing theconversion, light is propagated through a second optics section havingfirst and second eigenpolarization states.

Still another aspect of the invention comprises a method of propagatinglight. Light having first and second orthogonal polarization componentsis propagated through first optics comprising one or more cubiccrystalline optical elements. The first optics has fast and sloweigenpolarization states. The first and second orthogonal polarizationcomponents correspond to the fast and slow eigenpolarization states. Thelight is propagated through second optics comprising one or more cubiccrystalline optical elements. The second optics has fast and sloweigenpolarization states substantially similar in magnitude andorientation to the respective fast and slow eigenpolarization states ofthe first optics. Prior to propagating the light through the secondoptics, the polarization of the light is altered such that the first andsecond orthogonal polarization components correspond to the slow andfast eigenpolarization states, respectively, of the second optics.

Another aspect of the invention comprises a method which includestransmitting a beam of light having a polarization corresponding to thesum of two orthogonal polarization states through at least onebirefringent optical element thereby introducing phase delay between theorthogonal polarization states of the beam of light. The polarization ofthe beam of light is rotated. The light having rotated polarization istransmitted through at least one birefringent element therebyintroducing additional phase delay between the orthogonal polarizationstates to reduce the relative phase difference between the polarizationstates of the beam of light.

Yet another aspect of the invention comprises a method for forming anoptical system with reduced polarization aberration. The method includesproviding a plurality of optical elements along a common optical pathand inserting polarization rotation optics in said common optical path.The optical system is thereby divided into first and second parts. Thefirst and second parts have associated therewith first and secondpolarization aberrations, respectively. The polarization rotation opticsrotates the polarization of light transmitted therethrough. The opticalelements and the polarization rotation optics are selected and arrangedto reduce net polarization aberrations produced by the plurality ofoptical elements.

Another aspect of the invention comprises a method of reducing theretardance caused by intrinsic birefringence in an optical systemcomprising cubic crystalline optical elements. This method comprisesintroducing polarization rotation optics into the optical system. Thepolarization rotation optics are configured to rotate the polarizationof a light beam passing therethrough by odd integer multiples of about90 degrees, such that retardance introduced into an optical beamtransmitted through at least one of the cubic crystalline opticalelement is substantially offset by retardance introduced into theoptical beam upon transmitting the beam through at least one of thecubic crystalline optical elements after rotating the polarization ofthe beam.

Another aspect of the invention comprises a photolithography tool. Thisphotolithography tool includes a light source outputting light forilluminating a reticle and condenser optics positioned to receive lightfrom the light source. The condenser optics are positioned to direct anoptical beam formed from the light through the reticle. Thephotolithography tool further comprises projection optics configured toform an image of the reticle onto a substrate. The projection opticscomprise one or more cubic crystalline lens elements receiving thedirected optical beam propagated through the reticle and polarizationrotation optics positioned along a common optical pathway with thereticle and the one or more cubic crystalline lens elements. The one ormore cubic crystalline lens elements has intrinsic birefringence whichintroduces retardance into the optical beam. The polarization rotationoptics rotates the polarization of the optical beam transmitted throughthe one or more cubic crystalline lens elements.

Another aspect of the invention comprises a method of forming asemiconductor device. In this method, a beam of light is propagatedthrough a reticle. An optical image of the reticle is formed bydirecting the beam of light into a first part of a projection lens. Thefirst part of the projection lens includes one or more refractiveoptical elements, which cause the beam of light to become aberrated as aresult of first polarization aberrations introduced by the first part ofthe projection lens. These first polarization aberrations result fromvariation in an optical property with polarization. The polarization ofthe beam of light is rotated. The beam of light is then propagatedthrough a second part of the projection lens. The second part of theprojection lens includes one or more refractive optical elements. Thissecond part of the projection lens is selected to introduce secondpolarization aberrations which at least partially cancel the firstpolarization aberrations, the second polarization aberrations alsoresulting from variation in an optical property with polarization. Asubstrate is positioned such that the optical image formed by the beamof light output by the projection lens, is formed on the substrate.

In another aspect of the invention, a semiconductor device is formedaccording to a process which includes depositing a photosensitivematerial over a semiconductor wafer, illuminating a mask pattern, andtransmitting a beam of light having first and second orthogonalpolarization states along an optical path from the mask pattern throughat least one optical element. The optical element has instrinsicbirefringence such that the first polarization state is phase delayedwith respect to the second polarization state. The first and secondorthogonal polarization states of said beam of light are rotated and thebeam of light, having rotated the first and second orthogonalpolarization states, is transmitted through at least one birefringentelement. In this manner, the second polarization state is phase delayedwith respect to the first polarization state to reduce the relativephase difference between the first and second orthogonal polarizationstates of the beam of light. After said beam of light is transmittedthrough the at least one birefringent element, the beam is projectedonto said photosensitive material over said semiconductor wafer.Portions of photosensitive material are removed to form a pattern in thephotosensitive material that resembles the mask pattern, and thesemiconductor wafer having the patterned photosensitive material thereonis processed.

Yet another aspect of the invention comprises a photolithography toolthat includes a light source outputting light for illuminating a reticleand condenser optics positioned to receive light from the light source.The condenser optics is positioned to direct an optical beam formed fromthe light through the reticle. The photolithography tool furthercomprises projection optics configured to form an image of the reticleonto a substrate. The condenser optics includes one or more cubiccrystalline optical elements which receive the light from the lightsource. The one or more cubic crystalline optical elements haveintrinsic birefringence which introduces retardance into the opticalbeam. The condenser further includes polarization rotation opticspositioned along a common optical pathway through the one or more cubiccrystalline optical elements. The polarization rotation optic rotatesthe polarization of the light transmitted through the one or more cubiccrystalline optical elements.

Another aspect of the invention comprises an optical system comprisingone or more cubic crystalline lens elements having intrinsicbirefringence and a substantially optically transmissive elementcomprising a cubic crystalline central portion and a clamp securedthereto. The cubic crystalline central portion has a birefringenceinduced by compressive force imparted by the clamp. This birefringenceincreases radially away from an optical axis passing through the centralportion. The compressive force produces an amount of radially increasingbirefringence to at least partially offset the intrinsic birefringenceof the one or more cubic crystalline lens elements. The substantiallyoptically transmissive element may comprise a lens element. The cubiccrystalline central portion may comprise cubic crystalline fluoridematerial such as cubic crystalline calcium fluoride. In variousembodiments, the birefringence may increase quadratically from theoptical axis. The clamp may also comprise a hoop. Furthermore, theoptical system may include polarization rotation optics. Additionally,in some embodiments, a common optical axis may extend through the one ormore cubic crystalline lens elements and through the substantiallyoptically transmissive element and the birefringence induced by thecompressive force may increase radially away from the common opticalaxis.

Another aspect of the invention comprises a method for reducingretardance in an optical beam passing through an optical systemcomprising one or more cubic crystal optical elements forming an opticalpath. In this method an amount of force is applied to at least one ofthe cubic crystalline optical elements to produce a stress-inducedbirefringence increasing in magnitude substantially symmetrically awayfrom a central axis passing therethrough. The amount of applied force isselected to produce a birefringence to reduce retardance in the opticalbeam passing therethrough. This stress-induced birefringence mayincrease monotonically with distance from the central axis. Thestress-induced birefringence may increase quadratically with distancefrom the central axis. In some embodiments, the method may furthercomprise selecting and orienting said optical elements so as to reducesaid retardance. Also, the method may include rotating the polarizationof the beam to reduce said retardance.

Yet another aspect of the invention comprises a method for reducingretardance in an optical beam propagating across an optical path throughan optical system comprising one or more cubic crystal lens elementsaligned along a common optical axis. The method comprises replacing oneof the cubic crystal lens elements having a first optical power with twoor more cubic crystal optical elements. The two or more cubic crystaloptical elements together have a second optical power substantiallymatching the first optical power. The two or more cubic crystal opticalelements may also comprise cubic crystal having crystal axes orienteddifferently. The two or more cubic crystal optical elements may comprisecubic crystal having different crystal axis substantially aligned alongthe common optical axis. One of the cubic crystal lens elements may bereplaced with a [100] and a [110] cubic crystal element havingrespective [100] and [110] cubic crystal axes substantially aligned withthe common optical axis. One of the cubic crystal lens elements may bereplaced with a [111] and a [110] cubic crystal element havingrespective [111] and [110] cubic crystal axes substantially aligned withthe common optical axis. Also, one of the cubic crystal lens elementsmay be replaced with a [100] and a [111] cubic crystal element havingrespective [100] and [111] cubic crystal axes substantially aligned withthe common optical axis. In some embodiments, the two or more cubiccrystal optical elements may comprise cubic crystal having substantiallythe same crystal axis substantially aligned along the common opticalaxis, and the method may further comprise rotating said optical elementsabout the optical axis to an orientation that reduces retardance in saidoptical beam. One of the cubic crystal lens elements may be replacedwith two [111] cubic crystal lens elements having respective [111] cubiccrystal axes substantially aligned with the common optical axis. Also,in various embodiments, the method may further comprise insertingpolarization rotation optics in the optical path to rotate thepolarization of the beam and to reduce beam retardance.

In still another aspect of the invention, an optical system that outputslight comprises first and second sections each comprising a plurality ofsymmetrically shaped calcium fluoride lens elements and a retardationreduction system between the first and second sections. Each of thecalcium fluoride lens elements is symmetrical about a respective opticalaxis passing therethough. The plurality of symmetrically shaped calciumfluoride lens elements are arranged along an optical path. Thesymmetrically shaped calcium fluoride lens elements in the first andsecond sections together comprise at least about 80% by weight [111]cubic crystalline calcium fluoride having a [111] crystal directionsubstantially parallel to the respective optical axis. This opticalsystem may comprise a photolithography system, for use for example, infabricating semiconductor and/or other devices. In various embodiments,the polarization reduction system reduces retardance produced by theplurality of symmetrically shaped calcium fluoride lens elements in eachof the first and second sections together, such that the retardance ofthe light output by said optical system onto a reference surface is lessthan or equal to about 0.020 waves rms at each location on the referencesurface. In some embodiments, the retardance of the light output by saidoptical system onto a reference surface is less than or equal to about0.010 waves rms at each location on the reference surface. Thisreference surface may correspond, for example, to the exit pupil of theoptical system, to a wafer, to the format of a photolithographyinstrument but it is not limited to these examples.

In still another aspect of the invention, an optical imaging systemincludes a plurality of first lens elements arranged along a commonoptical axis. The first lens elements comprise [111] cubic crystallinecalcium fluoride having a [111] crystal direction substantially alongthe common optical axis passing through the first lens elements. Theoptical imaging system further comprises a plurality of second lenselements arranged along the optical axis. The second lens elementscomprise material selected from the group consisting of [100] cubiccrystalline calcium fluoride having a [100] crystal directionsubstantially along the common optical axis passing through the secondlens element and [110] cubic crystalline calcium fluoride having a [110]crystal direction substantially along the common optical axis passingthrough the second lens element. The plurality of first lens elementsoutweigh the plurality of second lens elements at least by a ratio ofabout 4 to 1 and the plurality of first lens elements. The plurality ofsecond lens elements have positions, shapes, and rotational orientationsabout the common optical axis so that less than about 0.015 waves rms ofretardance is produced by the plurality of first lens element and theplurality of second lens elements together. This optical system maycomprise an optical lithography system.

In yet another aspect of the invention, an optical system comprises afirst plurality of [111] cubic crystalline lens elements, polarizationtransforming optics, and a second plurality of [111] cubic crystallinelens elements. The first plurality of [111] cubic crystalline lens arearranged along an optical path for receiving an optical beam having afirst polarization. The polarization transforming optics transform thefirst polarization of the optical beam into a second polarization. Thesecond plurality of [111] cubic crystalline lens elements are arrangedalong an optical path for receiving the optical beam having the secondpolarization. Each of the [111] cubic crystalline lens elements aresymmetrical with respect to an optical axis passing though therespective lens element. Each of the [111] cubic crystalline lenselements also comprise [111] cubic crystalline calcium fluoride having a[111] crystal axis substantially parallel to an optical axis passingthrough the respective lens elements. Furthermore, the first pluralityof [111] cubic crystalline lens elements imparts a first retardance onthe optical beam and the second plurality of [111] optical elementsimparts a second retardance on the optical beam that at least partiallycompensates for the first retardance. In various embodiments, thisoptical system may be a photolithography system.

Another aspect of the invention comprises a method of reducingretardance in an optical beam propagating through at least one [111]optical element, the optical beam having a polarization corresponding tothe sum of two orthogonal polarization states. In this method, thepolarization of the optical beam is altered after the optical beam haspropagated through the at least one [111] optical element and hasacquired a first phase shift between the two orthogonal polarizationstates. The optical beam having altered polarization is propagatedthrough at least one [111] optical element thereby imparting a secondphase shift between the two orthogonal polarization states that at leastpartially counters the first phase shift. This method may be employed toreduce retardance in optical lithography systems.

In still another aspect of the invention, an optical system comprises aplurality of calcium fluoride lens elements each having respectiveoptical axes. The plurality of calcium fluoride lens elements arealigned along an optical path for propagation of light therethrough.Each of the calcium fluoride lens elements in the optical systemcomprises cubic crystalline calcium fluoride that is aligned with its[111] lattice direction substantially parallel with the respectiveoptical axes. This optical system may be a photolithography system foruse for example in fabricating semiconductor devices.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention and advantagesthereof may be acquired by referring to the following description, takenin conjunction with the accompanying drawings in which like referencenumbers indicate like features and wherein:

FIG. 1 is a cross-sectional view of a projection optics for an exemplarylithography system comprising twenty-nine refractive optical elements;

FIG. 2 is a schematic diagram of an exemplary lithography systemincluding a condenser lens and projection optics;

FIG. 3A is a graphical representation of variation of birefringence axisorientation with respect to a cubic crystal lattice;

FIG. 3B is a graphical representation of variation of birefringencemagnitude with respect to a cubic crystal lattice;

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice;

FIG. 5A is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [110] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5B is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [100] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5C is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [111] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 6 shows cross-sectional view of an exemplary arrangement of anoptical system referred to as a Dyson system comprising a refractiveelement and a reflective element aligned along an optical axis;

FIGS. 7A and 7B are graphical illustrations showing the net retardanceacross the system exit pupil for field points at the center and edge ofthe field, respectively, for an optical system such as shown in FIG. 6,wherein the refractive element comprises cubic crystalline materialhaving with its [111] crystal axis aligned along optical axis;

FIGS. 8A and 8B are graphical illustrations of the retardance across thesystem exit pupil for field points at the center and edge of the field,respectively, for an optical system such as shown in FIG. 6, wherein therefractive element comprises cubic crystalline material having with its[100] crystal axis aligned along optical axis;

FIGS. 9A and 9B are graphical illustrations of the retardance across thesystem exit pupil for field points at the center and edge of the field,respectively, for an optical system such as shown in FIG. 6, wherein therefractive element comprises cubic crystalline material having with its[110] crystal axis aligned along optical axis;

FIG. 10 is a cross-sectional view of the lens depicted in FIG. 6additionally including a 45° non-reciprocal Faraday rotator used torotate the polarization to reduce the harmful effects of intrinsicbirefringence;

FIG. 11A is a graphical illustration of net retardance across the pupilfor the exemplary optical system shown in FIG. 10 with refractiveelement comprising cubic crystalline material with its [111] crystalaxis aligned substantially along the optical axis for the extreme fieldpoint.

FIG. 11B is a graphical illustration of net retardance across the pupilfor the exemplary optical system shown in FIG. 10 with refractiveelement comprising cubic crystalline material with its [110] crystalaxis aligned substantially along the optical axis for the extreme fieldpoint.

FIG. 12 shows schematic cross-sectional view of an exemplary mixing rod,a non-imaging optical element;

FIG. 13 shows the net retardance across the exit pupil of the mixing roddepicted in FIG. 12 comprising cubic crystalline material with the [111]crystal axis aligned with and corresponding to the optical axis of themixing rod assuming that the reflections from the walls of theintegrating rod do not change the polarization state of the lightpropagating therein;

FIG. 14 depicts the polarization state of light across the exit pupilwhen a uniformly circularly polarized beam is incident on the entranceface of the mixing rod;

FIG. 15 is a schematic cross-sectional view of the mixing rod of FIG. 12further including a 90° polarization rotator centrally disposed withinthe mixing rod, the rotator possibly comprising a pair of quarterwaveplates on opposite sides of a halfwave plate;

FIG. 16 is a plot, on axis of angle (in degrees) and retardance error(in degrees) of the magnitude of retardance error as a function of angleof incidence for 1 and 3 millimeter thick quarter wave plates surroundedby air;

FIG. 17 is a graphical illustration of the net retardance across theexit pupil of the mixing rods shown in FIG. 15, which demonstrates thereduction of the net retardance resulting from introduction of thepolarization rotator in the optical system;

FIG. 18 shows the polarization state of the light across the exit pupilwhen a uniformly circularly polarized beam is incident on the entranceface of the mixing rod shown in FIG. 15, which includes the polarizationrotator;

FIGS. 19A and 19B are graphical illustrations of the net retardanceacross the pupil for central and extreme field points, respectively, forthe lens depicted in FIG. 1 wherein the optical elements comprise cubiccrystalline material with crystal axes substantially identically alignedin three dimensions, with the optical axis extending along the [110]crystal lattice direction computed using a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 20A and 20B are graphical illustrations of the net retardanceacross the pupil for central and extreme field points, respectively, forthe lens depicted in FIG. 1 wherein the optical elements comprise cubiccrystalline material with crystal axes substantially identically alignedin three dimensions, with the optical axis extending along the [100]crystal lattice direction computed using a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 21A and 21B are graphical illustrations of the net retardanceacross the pupil for central and extreme field points, respectively, forthe lens depicted in FIG. 1 wherein the optical elements comprise cubiccrystalline material with crystal axes substantially identically alignedin three dimensions, with the optical axis extending along the [111]crystal lattice direction computed using a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIG. 22 is a schematic illustration showing the exemplary lens depictedin FIG. 1, in which the twenty-nine optical elements comprise cubiccrystals having crystal axes substantially identically aligned in threedimensions, with the optical axis extending along the [100] crystallattice direction, further comprising −90° and 90° polarizationrotators;

FIGS. 23A and 23B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,due to intrinsic birefringence of the optical elements between the −90°and 90° polarization rotators for the exemplary lens depicted in FIG.22;

FIGS. 24A and 24B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,due to intrinsic birefringence of the elements between the 90°polarization rotator and the image plane for the exemplary lens depictedin FIG. 22;

FIGS. 25A and 25B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for all lens elements and the 90° polarization rotator excluding theretardance of the −90° polarization rotator for the exemplary lensdepicted in FIG. 22;

FIGS. 26A and 26B are graphical illustrations showing net retardanceacross the pupil at the central and extreme field points, respectively,for all elements and the 90° and −90° polarization rotators for theexemplary lens depicted in FIG. 22;

FIG. 27 is a schematic illustration showing the exemplary lens depictedin FIG. 22, in which the twenty-nine optical elements comprise cubiccrystalline material substantially having crystal axes substantiallyidentically aligned in three dimensions, with the optical axis generallyalong the [100] crystal lattice direction, including −90° and 90°polarization rotators and an element which has a hoop applied stress toinduce radial stress birefringence therein;

FIG. 28A is a contour plot showing the radial variation in birefringencein the first lens element having a hoop applied stress to induce radialstress birefringence therein in the exemplary lens depicted in FIG. 27,in which the variation is assumed to follow a quadratic profile with apeak birefringence of −6.95 mm/cm.

FIGS. 28B and 28C are graphical illustrations showing retardance acrossthe pupil at the central and extreme field points, respectively, due tothe birefringence induced by the hoop applied stress to the first lenselement following the reticle;

FIGS. 29A and 29B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for all elements, including the 90° and −90° rotators and the retardanceproduced by applying a hoop stress to the first element following thereticle for the exemplary lens depicted in FIG. 27;

FIG. 30 is a plot on axis of radius (in millimeters) and retardance (inwaves) illustrating the radial retardance variation across an exemplaryoptical element when a compressive hoop stress is applied around theperimeter of the element;

FIG. 31A is perspective view of a polarization rotator for rotating thepolarization of any arbitrary polarization state by about 90° about thepropagation direction.

FIG. 31B is a plot of the variation in residual retardance for a quarterwave plate as a function of numerical angle, sin θ, (from 0.0 to 0.5)and peak stress birefringence magnitude (from 1×10⁻⁶ to 1×10⁻³) for apolarization rotator constructed from single order wave plates employingstress induced birefringence;

FIG. 32 is a cross-sectional view of an exemplary large formatrefractive projection lens comprising twenty-eight refractive opticalelements comprising cubic crystalline material;

FIGS. 33A, 33B, 33C, and 33D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 32;

FIG. 33A shows the wavefront error for an input polarization in the Xdirection (used with an exit pupil analyzer in the X direction) for thecentral field point;

FIG. 33B shows the wavefront error for an input polarization in the Xdirection (used with an exit pupil analyzer in the X direction) for theextreme field point;

FIG. 33C shows the wavefront error for an input polarization in the Ydirection (used with an exit pupil analyzer in the Y direction) for thecentral field point;

FIG. 33D shows the wavefront error for an input polarization in the Ydirection (used with an exit pupil analyzer in the Y direction) for theextreme field point;

FIGS. 34A and 34B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 32 for centraland extreme field points, respectively, in which all elements are cubiccrystals with crystal axes substantially identically aligned in threedimensions, with the optical axis extending generally along the [110]crystal lattice direction computed for a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 35A and 35B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 32 at centraland extreme field points, respectively, in which all elements are cubiccrystals with crystal axes substantially identically aligned in threedimensions, with the optical axis extending generally along the [100]crystal lattice direction computed for a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 36A and 36B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 32 at centraland extreme field points, respectively, in which all elements are cubiccrystals with crystal axes substantially identically aligned in threedimensions, with the optical axis extending generally along the [111]crystal lattice direction computed for a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIG. 37 is a schematic illustration showing the exemplary lens depictedin FIG. 32, in which all the refractive optical elements comprise cubiccrystalline material with crystal axes substantially identically alignedin three dimensions, with the optical axis extending along the [110]crystal lattice direction, comprising −90° and 90° polarization rotatorswith the two elements closest to the wafer derived by splitting a singleoptical element, and having a toroidal surface;

FIGS. 38A and 38B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for the optical elements between the −90° and 90° polarization rotatorsfor the exemplary lens depicted in FIG. 37;

FIGS. 39A and 39B are graphical illustrations showing net retardanceacross the pupil at the central and extreme field points, respectively,for the optical elements between the 90° polarization rotator and theimage plane for the exemplary lens depicted in FIG. 37;

FIGS. 40A and 40B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for all elements and the 90° and −90° polarization rotators for theexemplary lens depicted in FIG. 37;

FIGS. 41A, 41B, 41C, and 41D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 37;

FIG. 41A shows the wavefront error for an input polarization in the Xdirection (used with an exit pupil analyzer in the X direction) for thecentral field point;

FIG. 41B shows the wavefront error for an input polarization in the Xdirection (used with an exit pupil analyzer in the X direction) for theextreme field point;

FIG. 41C shows the wavefront error for an input polarization in the Ydirection (used with an exit pupil analyzer in the Y direction) for thecentral field point;

FIG. 41D shows the wavefront error for an input polarization in the Ydirection (used with an exit pupil analyzer in the Y direction) for theextreme field point;

FIG. 42 is a schematic illustration showing an exemplary large formatcatadioptric projection lens comprising nineteen powered refractiveoptical elements and one powered reflective optical element;

FIGS. 43A and 43B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 42 for centraland extreme field points, respectively, in which the nineteen poweredrefractive optical elements comprise cubic crystals with crystal axessubstantially identically aligned in three dimensions, with the opticalaxis extending generally along the [110] crystal lattice directioncomputed for a peak birefringence magnitude corresponding to that ofcalcium fluoride at a wavelength of 157 nm;

FIGS. 44A and 44B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 42 for centraland extreme field points, respectively, in which the nineteen poweredrefractive optical elements comprise cubic crystals with crystal axessubstantially identically aligned in three dimensions, with the opticalaxis extending along the [100] crystal lattice direction computed for apeak birefringence magnitude corresponding to that of calcium fluorideat a wavelength of 157 nm;

FIGS. 45A and 45B are graphical illustrations showing net retardanceacross the pupil for the exemplary lens depicted in FIG. 42 for centraland extreme field points, respectively, in which the nineteen poweredrefractive optical elements comprise cubic crystals with crystal axessubstantially identically aligned in three dimensions, with the opticalaxis extending along the [111] crystal lattice direction computed for apeak birefringence magnitude corresponding to that of calcium fluorideat a wavelength of 157 nm;

FIG. 46 is a schematic cross-sectional view showing an exemplary lenssimilar to that depicted in FIG. 29, with twenty powered refractiveelements comprising cubic crystalline material with crystal axessubstantially identically aligned in three dimensions, with the opticalaxis extending along the [111] crystal lattice direction, furthercomprising −90° and 90° polarization rotators, with the optical elementclosest to the wafer derived by splitting a single powered refractiveoptical element, and having a toroidal surface.

FIGS. 47A and 47B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for the optical elements between the −90° and 90° polarization rotatorsfor the exemplary lens depicted in FIG. 46;

FIGS. 48A and 48B are graphical illustrations showing net retardanceacross the pupil for the central and extreme field points, respectively,for the optical elements between the 90° polarization rotator and theimage plane for the exemplary lens depicted in FIG. 46; and

FIGS. 49A and 49B are graphical illustrations showing net retardanceacross the pupil at the central and extreme field points, respectively,for all elements and the 90° and −90° polarization rotators for theexemplary lens depicted in FIG. 46.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

It is well-known that cubic crystalline materials like calcium fluorideare favored in lithography systems, such as the high performancephotolithographic tools used in the semiconductor manufacturingindustry. These crystalline materials are substantially transmissive toshort wavelength UV light, which provides for high optical resolution.It is also well-known, however, that these cubic crystalline materialsexhibit intrinsic birefringence, i.e., an inherent anisotropy inrefractive index.

Birefringence, or double-refraction, is a property of refractivematerials in which the index of refraction is anisotropic, that is, theindex of refraction and thus the phase velocity is different fordifferent polarizations. For light propagating through a birefringentmaterial, the refractive index varies as a function of polarization andorientation of the material with respect to the polarization and thusthe propagation direction. Unpolarized light propagating through abirefringent material will generally separate into two beams withorthogonal polarization states. These beams may be referred to aseigenpolarization states or eigenpolarizations. The two beams propagatethrough the material with a different phase velocity. As the lightpasses through a unit length of the birefringent material, thedifference in phase velocity for the two ray paths will produced a phasedifference between the polarizations, which is conventionally referredto as retardance. These two states having different phase velocities maybe referred to as the slow and fast eigenpolarization states.

Birefringence is a unitless quantity, although it is common practice inthe lithography community to express it in units of nanometer percentimeter (nm/cm). Birefringence is a material property, whileretardance is an optical delay between polarization states. Theretardance for a given ray through an optical system may be expressed innanometers (nm), or it may be expressed in terms of number of waves of aparticular wavelength.

In uniaxial crystals, such as magnesium fluoride or crystal quartz, thedirection through the birefringent material in which the two orthogonalpolarizations travel with the same velocity is referred to as thebirefringence axis. The term optic axis is commonly used interchangeablywith birefringence axis when dealing with single crystals. In systems oflens elements, the term optical axis usually refers to the symmetry axisof the lens system. To avoid confusion, the term optical axis will beused hereinafter only to refer to the symmetry axis in a lens system.For directions through the material other than the birefringence axis,the two orthogonal polarizations will travel with different velocities.For a given incident ray upon a birefringent medium, the two refractedrays are commonly described as the ordinary and extraordinary rays. Theordinary ray is polarized perpendicular to the birefringence axis andrefracts according to Snell's Law, and the extraordinary ray ispolarized perpendicular to the ordinary ray and refracts at an anglethat depends on the direction of the birefringence axis relative to theincident ray and the amount of birefringence. In uniaxial crystals, thebirefringence axis is oriented along a single direction, and themagnitude of the birefringence is constant throughout the material.Uniaxial crystals are commonly used for optical components such asretardation plates and polarizers.

In contrast, however, cubic crystals have been shown to have both abirefringence axis orientation and magnitude that vary depending on thepropagation direction of the light with respect to the orientation ofthe crystal lattice. In addition to birefringence, which is thedifference in the index of refraction seen by the twoeigenpolarizations, the average index of refraction also varies as afunction of angle of incidence, which produces polarization independentphase errors.

Optical elements constructed from a cubic crystalline material, maycause a wavefront to be retarded as a result of the intrinsicbirefringence of the optical element. Moreover, the retardance magnitudeand orientation at a given point on the wavefront may vary, because thelocal propagation angle with respect to the material varies across thewavefront. Such variations in retardance across the wavefront may bereferred to as “retardance aberrations.” Retardance aberrations split auniformly polarized or unpolarized wavefront into two wavefronts withorthogonal polarizations. Again, these orthogonal wavefronts correspondto the eigenpolarization states. Each of the orthogonal wavefronts willexperience a different refractive index, resulting in differentwavefront aberrations.

Optical elements comprising cubic crystalline material thereforeintroduce additional aberrations that are correlated with polarization.These aberrations are generally referred to herein as polarizationaberrations and include the retardance aberrations described above whichresult from intrinsic birefringence in cubic crystalline materials.Additionally, these polarization aberrations include diattenuation, thevariation in optical transmission with polarization.

In cubic crystalline material, these polarization aberrations aresignificant enough to affect image quality in optical systems such asphotolithography system used in semiconductor fabrication processing.Accordingly, methods and apparatus for reducing these aberrations havesignificant value.

For ease of description, the cubic crystalline materials have crystalaxis directions and planes described herein using the well-known Millerindices, which are integers with no common factors and that areinversely proportional to the intercepts of the crystal planes along thecrystal axes. Lattice planes are given by the Miller indices inparentheses, e.g. (100), and axis directions in the direct lattice aregiven in square brackets, e.g. [111]. The crystal lattice direction,e.g. [111], may also be referred to as the [111] crystal axis of thematerial or optical element. The (100), (010), and (001) planes areequivalent in a cubic crystal and are collectively referred to as the{100} planes.

As discussed above, for cubic crystalline materials, the magnitude ofbirefringence depends on the direction of light propagation through thecrystal with respect to the orientation of the crystal axes. Forexample, light propagating through an exemplary cubic crystallineoptical element along the [110] crystal axis experiences the maximumbirefringence, while light propagating along the [100] crystal axisexperiences no birefringence.

Unfortunately, when constructing optical systems from cubic crystallinematerials such as calcium fluoride, the cost of the optical elementscontributes significantly to the total cost of these optical systems. Inparticular, the expense of the materials used to fabricate therefractive optical elements drives up the cost. Moreover, opticalelements comprising calcium fluoride having an optical axis directedalong the [100] crystalline directions, which has the least intrinsicbirefringence, is the most expensive to fabricate. Blanks for creatingrefractive elements having an optical axis corresponding to the [110]are also expensive. In contrast, calcium fluoride grown (or cleaved) inthe [111] direction is significantly less expensive to fabricate.However, as described above, optical elements having an optical axisgenerally coinciding with the [111] direction of the crystallinematerial although least expensive, possess intrinsic birefringence whichintroduces wavefront aberrations that degrade performance of opticalsystems such as image quality and resolution. Although both [100] and[111] optical elements have zero birefringence along their respectiveoptical axes, for [100] optical elements, the birefringence increasemore slowly for rays further and further off-axis.

FIG. 1 is a schematic illustration of a projection optics section of anexemplary lithography system. The optical system 100 shown in FIG. 1 issubstantially similar to the optical system shown and described EuropeanPatent Application No. 0 828 172 by S. Kudo and Y. Suenaga, the contentsof which are incorporated herein by reference in their entirety. Thisexemplary optical system 100 is a large format refractive projectionlens having an NA of 0.75, a peak wavelength of 193.3 nm and providing a4× reduction. Such an optical system is intended to be exemplary onlyand other optical imaging systems and non-imaging systems may be used inother embodiments. The optical system 100, however, may be theprojection optics section of a lithography tool in one preferredembodiment. As shown in FIG. 1, the projection lens 100 is disposedbetween a reticle 102 and a substrate 104. The reticle 102 may beconsidered to correspond to the object field with the substrate 104 inthe image field of the projection lens 100.

The optical system 100 shown is a lens system, commonly referred tocollectively as a “lens,” comprising a plurality of, i.e., twenty-nine,individual lens elements L1-L29, an optical axis 106, and aperture stop(AS) 108. The reticle 102 includes a mask pattern, which is to beprojected onto a surface 110 of the substrate 104. Substrate 104 may,for example, be a semiconductor wafer used in the semiconductormanufacturing industry, and surface 110 may be coated with aphotosensitive material, such as a photoresist commonly used in thesemiconductor manufacturing industry. Other substrates may be usedaccording to other embodiments and applications. Reticle 102 may be aphotomask suitable for various microlithography tools. Generallyspeaking, the reticle or photomask, hereinafter referred to collectivelyas reticle 102, includes a pattern in the object field. The pattern mayfor example be clear and opaque sections, gray scale sections, clearsections with different phase shifts, or a combination of the above.Light is propagated through the pattern, and the pattern is projectedthrough the lens system 100 and onto surface 110 of substrate 104. Thepattern projected from the reticle 102 onto substrate surface 110 may beuniformly reduced in size to various degrees such as 10:1, 5:1, 4:1 orothers. The optical system 100 may have a numerical aperture, NA, of0.75, but is not so limited. Systems having other numerical apertures,such as for example between about 0.60 to 0.90 or beyond this range areconceivable.

The arrangement of the plurality of lens elements L1-L29, is intended tobe exemplary only and various other arrangements of individual lenselements having various shapes and sizes and comprising differentmaterials may be used according to other exemplary embodiments. Theelement thicknesses, spacings, radii of curvature, asphericcoefficients, and the like, are considered to be the lens prescription.This lens prescription is not limited and will vary with application,performance requirements, cost, and other design considerations.

The optical system 100 shown in FIG. 1, includes twenty-nine individuallenses or powered refractive optical elements. Each of these arepreferably substantially optically transmissive at the wavelength ofoperation. More or less optical elements may be included in otherdesigns. In other embodiments, these elements may be powered orunpowered, refractive, reflective, or diffractive and may be coated oruncoated. The individual lens elements, L1-L29, are arranged along thecommon optical axis 106 that extends through the lens 100. In theexemplary embodiment of FIG. 1, this optical axis 106 is linear.

In the case where the optical system 100 comprises a plurality ofindividual lens elements L1-L29, or other optically transmissivecomponents, preferably one or more comprises cubic crystalline material.Cubic crystalline materials such as for example single crystal fluoridematerials like strontium fluoride, barium fluoride, lithium fluoride,and calcium fluoride may be used. Calcium fluoride is one preferredmaterial for operation with ultraviolet (UV) light. In an exemplaryembodiment, most or even all of the cubic crystalline optical elementsare formed of the same cubic crystalline material. This cubiccrystalline material may also have the same crystallographic orientationwith respect to the optical axis of the lens 100. In one preferredembodiment, a majority of the lens elements comprise cubic crystal suchas cubic crystal calcium fluoride having a <111> crystal axissubstantially aligned with the optical axis, as these crystals are lessexpensive than other crystallographic directions. In one embodiment, allof the lens or powered optical elements comprise <111> crystal.Non-powered transmissive optical elements, if any, may also comprise<111> crystal. The lens 100 may also include lens elements, which areformed of non-cubic crystalline material such as low-OH fused silica,also known as dry fused silica.

FIG. 2 is a schematic illustration showing the optical system 100functioning as the projection optics section within a larger lithographytool 50. FIG. 2 shows an optical source 112 and the substrate 104. Thereticle 102 is disposed between condenser optics 114 and projectionoptics 100. The optical field of reticle 102 may be of variousdimensions. Each of projection optics 100 and condenser optics 114 mayinclude an aperture stop and a plurality of lens elements, windows, andother refractive, reflective, catadioptric, and diffractive members. Thelithography tool 50 shown in FIG. 2 is aligned along the optical axis106, which in this case is linear. This lithography tool 50 may be awafer stepper, projection printer, or other photolithography ormicrolithography tool used in the semiconductor industry. Thelithography tool 50 may likewise be a scanning optical system, astep-and-repeat optical system or other microlithography or projectionoptics system. In a scanning-type optical system, a pattern on reticle102 is projected and scanned onto corresponding sections of surface 110of substrate 104. In a step-and-repeat optical system, such as aconventional wafer stepper, the pattern on reticle 102, is projectedonto multiple different portions of surface 110 in a plurality ofdiscrete operations. In either case, the reticle pattern includesvarious field points which are projected onto surface 110simultaneously.

The pattern printed on reticle 102 may be used to create a circuitpattern on surface 110 for an integrated circuit device being fabricatedon the substrate 104. The pattern may be projected onto a photosensitivematerial formed on surface 110 to create an exposure pattern. Theexposure pattern may be developed using conventional means, to produce aphoto-pattern in the photosensitive material. The photo-pattern may betranslated into the substrate 104 by etching or other method. Aplurality of layers of materials can be deposited thereon. The surface110 may be one of the layers and the photo-pattern formed on the layer.Etching or other techniques may be used to translate the photo-patterninto the layer. Similarly-formed photo-patterns may be used to enablespatially selective doping using known methods such as ion implantation.In this manner, multiple photolithographic operations, may be used toform various patterns in various layers to create a completedsemiconductor device such as an integrated circuit. An advantage of theinnovative techniques described herein is that images formed on thesubstrate 104 have sufficiently low aberration to enable preciselydimensioned and aligned device features to be created having reducedsizes.

In one exemplary scanning optical system, the optical field of reticle102 which is projected and scanned onto the substrate surface 110 has aheight of about 26 millimeters and a width of a few millimeters. Otherfield dimensions may be used which are suitable for the specificapplications and may depend on the type of lithography tool in which theprojection optics are included. Similarly, the format at the image planewhere the wafer is located may vary as well.

The optical source 112 produces light that is subsequently shaped andconditioned by condenser lens 114. The optical wavelength of source 112may vary, and may be no greater than 248 nanometers in some cases. Inone preferred embodiment, light having a wavelength of about 157nanometers may be used. The optical source 112 may produce linearlypolarized light. One optical source that produces linearly polarizedlight is an excimer laser. In other embodiments, the optical source 112may produce light having other polarizations or which is substantiallynon-polarized. A KrF excimer laser operating at about 248 nm, an ArFexcimer laser operating at about 193 nm, or an F₂ excimer laseroperating at about 157 nm, are examples of various optical sources 112.

The light produced by the optical source 112 is shaped and conditionedby the condenser lens 114 and propagated through the reticle 102 and theprojection optics 100 to project an image of the reticle 102 orphotomask onto the substrate 110. This light may be described as a lightbeam comprised of a plurality of rays. In accordance with convention,the marginal ray is the ray from the point on the object field 102intersecting the optical axis 106, to the edge of the aperture 108 andalso intersects the axis 106 at the image field 104. The chief ray isthe ray from a given field point that passes through the center of theaperture stop 108 and system pupils in the optical system 100. For anobject field point located where the optical axis 110 intersects thereticle 102, the chief ray travels along the optical axis 106. Lightrays emanating from an individual object field point on the reticle orphotomask 102 correspond to a wavefront that is propagated through theprojection lens 100 and are focus down to a corresponding image fieldpoint at the substrate 104. The full image field is therefore generatedby a plurality image field points with corresponding wavefrontsassociated therewith.

As describe above, these wavefronts may be aberrated as a result ofretardance arising from intrinsic birefringence which has magnitude andorientation that varies with direction in cubic crystalline materials.FIG. 3A is a three-dimensional vector plot showing the spatial variationin birefringence axis orientation within a material having a cubiccrystalline lattice. The cubic crystalline lattice may be that ofcalcium fluoride, for example. The crystal axis directions shown in FIG.3A as well as in FIG. 3B are described using Miller indices. FIG. 3B isa three-dimensional plot corresponding to a quadrant of the vector plotshown in FIG. 3A, and depicts the corresponding magnitude of theintrinsic birefringence. It can be seen that the localized magnitude andaxis of the birefringence vary spatially throughout the crystal in aknown fashion. It can also be seen that, depending on the directionalong which light travels through such a cubic crystalline material, thebirefringence magnitude and the orientation of the birefringence axisrelative to the direction of propagation will vary. FIG. 3B representsan octant of the crystal lattice; the extension of this diagram to allpossible directions through the crystal gives twelve directions withmaximum birefringence, herein referred to as birefringence lobes.

The crystalline material can therefore be advantageously cut along agiven plane and arranged such that light normal to that plane travelsalong a chosen axis direction. For example, light traveling along the[100] crystal axis 130 (i.e. along the [100] crystal lattice direction),which is oriented normal to the (100) crystal lattice plane 132, sees afixed and deterministic localized intrinsic birefringence. Thebirefringence magnitude and birefringence axis direction encountered bya given ray therefore varies as a function of the direction along whichthe light ray travels through the crystal.

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice. Thecubic crystalline lattice may be that of calcium fluoride, for example.FIG. 4 includes the peak intrinsic birefringence directions along the[101], [110], and [011] lattice directions, indicated by lines 142, 144,and 146, respectively. Line 140 represents the [111] crystal axisdirection, which corresponds to a direction through the crystal withoutintrinsic birefringence.

FIGS. 5A, 5B, and 5C are schematic representations of the variations inbirefringence magnitude and birefringence axis orientation in angularspace for optical axis 106 orientations in the [110], [100], and [111]lattice directions, respectively, for the cubic crystalline latticestructure shown in FIG. 4. The center of the plot represents thebirefringence encountered by a ray traveling along the indicated crystalaxis and normal to the plane of the illustration. Birefringence depictedat increased radial distance from the center represents thebirefringence for rays at increased angles of propagation with respectto the optical axis 106. These plots, therefore can be used to visualizethe birefringence encountered from a plurality of rays emanating from apoint, e.g. on the optical axis 106 through a lens element comprisingfor example [111] material. The ray through the optical axis 106propagates in the [111] direction through the center of the lens elementand encounters a birefringence with magnitude and orientation specifiedat the center of the plot. A ray emanating from the point on the axisbut angled will experience birefringence specified by the directionindicated on these plots. In each of FIGS. 5A-5C, the localizedbirefringence axis is indicated by the direction of lines plotted on asquare grid, and the magnitude is indicated by the relative length ofthe lines.

The variation of birefringence magnitude in FIGS. 5A-5C is characterizedby several lobes, also referred to as nodes, distributed azimuthally inwhich the birefringence is maximized. Each of FIGS. 5A-5C shows peakintrinsic birefringence lobes with respect to the various crystal axisdirections in the cubic crystalline lattice shown in FIG. 4. The spatialorientation of the cubic crystalline lattice is indicated by the otherrelated crystalline lattice directions indicated by the arrows. Forexample, in FIG. 5A in which the center represents birefringenceencountered by a ray traveling along the [110] crystal axis, a raytraveling along the [101] lattice direction is at a greater angle withrespect to the [110] crystal axis than a ray traveling along the [111]lattice direction; these ray angles are at 60° and 35.3°, respectively.This is indicated by the [101] arrowhead positioned at a greater radialdistance from center than the [111] arrowhead. The relative azimuthaldirections of the indicated [100], [101], and [111] lattice directionsare as shown in FIG. 4. This description applies to FIGS. 5B and 5C aswell.

Referring to FIGS. 5A-5C, in each case, the indicated crystal axis isthe direction normal to the plane of the paper and at the center of eachof the respective figures. FIG. 5A shows intrinsic birefringence withrespect to the [110] lattice direction, including peak intrinsicbirefringence lobes 150A, 150B, 150C and 150D, each which forms an angleof 60° with respect to the [110] crystal axis direction. Intrinsic [110]birefringence also includes a central birefringence node. FIG. 5B showsintrinsic birefringence with respect to the [100] lattice direction,including peak birefringence lobes 152A, 152B, 152C and 152D each ofwhich forms a 45° angle with respect to the [100] crystal axisdirection. There are also peaks along the diagonals at 90° not depicted.FIG. 5C shows intrinsic birefringence along the [111] lattice directionand which includes peak birefringence lobes 154A, 154B, and 154C, eachof which forms an angle of 35.3° with respect to the [111] crystallattice direction.

The crystal lattice and resulting intrinsic birefringence lobes withrespect to the crystal axes such as shown in FIGS. 5A-5C, correspond tothe exemplary case in which the cubic crystals are negative cubiccrystals; that is the ordinary refractive index is greater than theextraordinary index, so the birefringence, n_(e)-n_(o), is negative.Calcium fluoride is an example of a negative cubic crystal. For positivecubic crystals, the patterns would be substantially similar except thelines would be each rotated by 90 degrees about their midpoints. Itshould be understood that other cubic crystalline optical elements suchas barium fluoride, lithium fluoride, and strontium fluoride as well asother materials might be used to form optical elements. With respect toany cubic crystalline material used, the variations in the intrinsicbirefringence direction and magnitude can be measured, or calculatedusing computer modeling. Furthermore, the variations in intrinsicbirefringence direction and magnitude of an optical material may also bemeasured. Graphical representations of the variations in birefringencemagnitude and axis orientations similar to those shown in FIGS. 5A-5C,can be similarly generated for each of the aforementioned cubiccrystalline materials.

Referring again to FIG. 1, it can be understood that if each ofindividual lens elements L1-L29 or optical elements is formed of thesame cubic crystalline optical material such as calcium fluoride and theindividual elements L1-L29 are arranged along a common optical axis 106and aligned such that each of individual elements L1-L29 that isconstructed from a cubic crystalline material, includes substantiallythe same three dimensional lattice orientation with respect to theoptical axis 106, then the net retardance of the lens system 100 willhave a retardance that varies across the system exit pupil in a similarmanner to the angular intrinsic birefringence variation shownschematically in FIGS. 5A-5C.

Example 1

FIG. 6 shows an exemplary optical system 160 usable for lithographicapplications that is based on a Dyson catadioptric lens comprising asingle refractive element 162 and single reflective element 164 alignedalong an optical axis 165 [Refs. J. Dyson, “Unit magnification opticalsystem without Seidel aberrations,” J. Opt. Soc. Am., Vol. 49, p. 713(1959), as described in R. Kingslake, Lens Design Fundamentals, AcademicPress, Inc. (1978)] In one preferred embodiment, the refractive opticalelement comprises cubic crystalline material. This refractive element162 has first planar surface 166 and second curved surface 168. Thereflective element 164 also has a curved reflective surface 170.

A notable feature of the Dyson design is that the object and imagefields 172, 174 are coplanar and located at the center of curvature, C,of the curved surfaces on the refractive and reflective elements 160 and162. Preferably, the radius of curvature, R₁, of the refractive element162 is (n_(o)−1)/n_(o) times the radius of curvature, R₂ of thereflective surface 170, where n_(o) is the ordinary index of refractionof the refractive element 162. These design specifications provide adesign that is corrected for Petzval curvature and third order sphericalaberration, coma, and sagittal astigmatism. Simulations were performedfor an exemplary Dyson system having a numerical aperture of 0.20 andobject and image heights, H and H′, of 7 and −7 mm, respectively. Thewavelength of light was assumed to 157.63 nm. Of course othercurvatures, thicknesses, materials, as well as other object and imageheights are possible. The optical system 160 may also be used at otherwavelengths may and may have a different numerical aperture in otherembodiments. At this wavelength, however, the ordinary index ofrefraction, n_(o), is assumed to be 1.5587. The dimensions of theexemplary system 160 used in the simulations are listed in Table 1.

TABLE 1 Radius of Surface Curvature Thickness Glass 1 Infinite 0.000 2−100.000 100.000 CaF₂ Stop −278.987 −178.987 Reflection 4 −100.000−100.000 CaF₂ Image Infinite 0.000

Cubic crystalline element 160 is assumed to have a birefringencemagnitude, n_(e)-n_(o), of −12×10⁻⁷, corresponding to the intrinsicbirefiingence of calcium fluoride measured at a wavelength of 157 nm assuggested in D. Krahmer, “Intrinsic Birefringence in CaF₂,” at CalciumFluoride Birefringence Workshop, Intl SEMATECH, Jul. 31, 2001.

When the effects of intrinsic birefringence associated with the cubiccrystalline lens material are taken into account, system performancedegrades significantly. FIGS. 7A and 7B are graphical illustrationsshowing the net retardance across the system exit pupil for field pointsat the center and edge of the field, respectively, when the refractiveelement 162, shown in FIG. 6, is aligned with its [111] crystal axisparallel with the optical axis 165.

In these plots, and the retardance pupil maps to follow, the retardanceis shown on a square grid across the system exit pupil for the opticalsystem of interest. As described above, the retardance will generallyvary across a wavefront propagating through a birefringent opticalsystem. Accordingly, the retardance will be different for differentlocations across a cross-section of the beam. The variation plotted inthese retardance maps corresponds to the exit pupil of the opticalsystem.

The retardance plots are described in general by ellipses, whichsometimes degenerate into lines that show one of the eigen-polarizationstates. As defined above, the eigen-polarization state is a polarizationstate that remains unchanged for a ray propagating through the opticalsystem at given pupil coordinates. The eigen-polarization in the plotsis the slow eigenpolarization state. The fast and the sloweigenpolarizations are orthogonal. The fast eigenpolarization statecorresponds to the eigenpolarization shown in the plot rotated 90° aboutits center. For example, if the local retardance, be it linear orelliptical, is in the vertical direction, the slow eigenpolarizationstate will be oriented in the vertical direction and the fasteigenpolarization state will be oriented in the horizontally. Thedirection of the ellipse is defined by its major axis; for a verticalellipse, the major axis is oriented in the vertical direction. We referto the major axis as the retardance axis. The size of the ellipse orlength of the line at a given pupil coordinate is proportional to therelative strength of the retardance, i.e., the phase shift between thefast and slow eigenpolarizations.

Also, for the lenses and corresponding retardance maps, the coordinatesare defined using a right-handed coordinate system such that the systemoptical axis is in the +Z direction from the object towards the imageplane, the +Y axis is in the vertical direction, and the +X direction isorthogonal to the Y and Z axes. For the exit pupil retardance andwavefront maps, the plots describe variations over an exit pupilreference sphere for a given field point using a Cartesian coordinatesystem, where the X and Y coordinates are coordinates on the referencesphere projected onto a plane perpendicular to the chief ray.

FIGS. 7A and 7B include the effects of intrinsic birefringence on theoptical system 160 depicted in FIG. 6. The object field height in FIG.7A is 0 mm and the object field height in FIG. 7B is 7 mm, correspondingto the center and edge field points, respectively. The peak retardancedue to intrinsic birefringence in this example is approximately 0.41waves at a wavelength of 157.63 nanometers.

FIG. 7A plots the retardance across the exit pupil for a beam of lightrepresented by a bundle of rays emanating from an object point on theoptical axis 165 through the system 160 to a location on the image field174 ideally also located on the optical axis 164. This beam andcorresponding bundle of rays fills the aperture and the exit pupil. Theretardance map of FIG. 7A corresponds to the retardance for rays at eachof the locations shown in the exit pupil. These retardance plots thusrepresent the retardance sampled across this particular beam at the exitpupil. The retardance may correspond to a wavefront at the exit pupilproduced by a point source on axis in the object field. Similarly, FIG.7B plots the retardance across the exit pupil for a beam of lightrepresented by a bundle of ray emanating from an off-axis object point,here 7 mm off axis, passing through the system 160 to a location on theimage field 174 also located off-axis. The beam and the correspondingbundle of rays also fills the aperture and the exit pupil. Theretardance map of FIG. 7B shows the retardance for rays at variouslocations in the exit pupil. As described above, this retardance maycorrespond to that of the wavefront at the exit pupil produced by apoint source at the off-axis field point, 7 mm off axis in the objectfield. This off-axis object field point may map, for example, into apoint on the edge of the format of a photolithography instrument. Theseretardance plots thus represent the retardance sampled across thisparticular beam at the exit pupil.

FIGS. 8A and 8B are graphical illustrations of the retardance of anotherexemplary embodiment of the lens system 160 shown in FIG. 6. In FIGS. 8Aand 8B, the net retardance across the system exit pupil, including theeffects of intrinsic birefringence, is depicted for field points at thecenter and edge of the field for a refractive element 162 comprisingcubic crystal having a [100] crystal axis along the optical axis 165.The peak retardance due to intrinsic birefringence in this example isapproximately 0.1 waves at a wavelength of 157.63 nanometers. The peakretardance for the [100] optical element 162 associated with FIGS. 8Aand 8B is thus smaller than the peak retardance for the [111] opticalelement 162 associated with FIGS. 7A and 7B.

FIGS. 9A and 9B are graphical illustrations of the retardance of anotherexemplary embodiment of crystal lattice orientation of the refractiveelement 162 shown in FIG. 6. In FIGS. 9A and 9B, the net retardanceacross the system exit pupil is depicted for field points at the centerand edge of the field with refractive element 162 comprising cubiccrystal material having a [110] crystal axis generally along the opticalaxis 165. The peak retardance due to intrinsic birefringence in thisexemplary arrangement is approximately 0.58 waves at a wavelength of157.63 nanometers, which is higher than the peak retardance for the[111] optical element 162 associated with FIGS. 7A and 7B and the peakretardance for the [100] optical element 162 associated with FIGS. 8Aand 8B. In the retardance pupil maps given in FIGS. 9A and 9B, and inothers to follow in which the net retardance exceeds a magnitude of ±0.5waves (i.e., π radian or 180°), the retardance is plotted “modulo 1wave.” It can therefore be seen that the retardance orientation rotatesby 90 degrees at one-half-wave intervals, i.e., the effect of a 0.75wave retarder at 0 degrees is the same as a 0.25 wave retarder at 90degrees.

Each of three preceding examples, as illustrated in FIGS. 7A-9B, showsthat the intrinsic birefringence produces large polarizationaberrations, namely, large retardance aberrations. The result is largewavefront aberrations, even with a single refractive element 162 used ata moderate numerical aperture. Without compensation, this aberrationstrongly exceeds the allowable wavefront error for photolithography ormany other imaging applications.

The retardance plots in FIGS. 7A-9B are for a single pass through therefractive optical element 162 corresponding to light propagating fromthe object field 172 through the refractive optical element 162 andtoward the reflective optical element 164. As discussed above, the imageplane 174 is superimposed on the object plane 172 and thus, in a Dysonsystem, image formation involves reflection of light rays off thereflective optical element 164 and back through the refractive opticalelement 162. With refractive element 162 oriented with either its [111],[100], or [110] crystal axis aligned substantially along the opticalaxis 14, the retardance produced by refractive element 162 for thecentral field point will have the same variation in magnitude andorientation across the pupil on the first and second passes through therefractive element 162, since each ray from the central field point isreflected back upon itself by reflective element 164. The retardanceintroduced in the first pass is thus matched to the retardanceintroduced in the second pass.

To reduce the retardance produced by the refractive element 162, whichcomprises cubic crystal, a non-reciprocal Faraday rotator 180 isinserted between refractive element 162 and reflective element 164, asdepicted in FIG. 10. Preferably, this non-reciprocal rotator 180provides an approximately 45° rotation to the polarization of lightpassing therethrough. (By non-reciprocal is meant that the rotator 180rotates polarization in the same direction, i.e., clockwise orcounter-clockwise, for light transmitted through the rotator 180 in botha first forward axial direction and a second reverse axial direction.Thus, the rotator will provide a rotation in the second pass that addsto the rotation introduced on the first pass. A reciprocal rotator, incontrast, would rotate the polarization in the counter-opposingdirections for light passing through the rotator in the forward andreverse axial directions; the two polarization rotations would thereforecancel out with no net polarization rotation.)

The Faraday rotator 180 alters the polarization state by rotating theconstituent polarizations by about 45° each time the beam passes throughthe rotator 180. For example, as is well known, linear or ellipticalpolarized light can be reduced to vertical and horizontal polarizationcomponents. Both these polarization components are rotated about thepropagation direction by approximately 45° upon respective first andsecond forward and reverse passes through the Faraday rotator 180.Because the beam travels through the 45° Faraday rotator 180 twicefollowing the first pass through refractive element 162, the rotator 180produces a net rotation of 90° for each constituent polarization statebefore the beam passes through refractive element 162 a second time.Accordingly, the above-mentioned horizontal component becomes verticallyoriented and the above-mentioned vertical component becomes horizontallydirected. The sum of the two components forms an aggregate polarizationcorresponding to the original linear or elliptical polarization staterotated by about 90° about the propagation direction.

Similarly, in the case where the light from the object has linearpolarization and is polarized along the horizontal, after first andsecond passes through the rotator 160, the horizontally polarized lightbecomes vertically polarized. For this example, in the first passhorizontally polarized light passes through the refractive opticalelement 160 and in the second pass, assuming no diattenuation,vertically polarized light having substantially the same magnitude asthe horizontally polarized light of the first pass is transmittedthrough the refractive optical element 162. In another example, lightfrom the object which is elliptically polarized with the major axis ofthe ellipse substantially aligned in the vertical direction, after firstand second passes through the rotator 160, becomes ellipticallypolarized light oriented horizontally. Thus, on the first pass throughthe refractive optical element 160, the elliptically polarized light isvertically oriented and upon the second reverse pass through therefractive element 162 is elliptically polarized with the major axisalong the horizontal. The constituent polarization components aresimilarly rotated by 90°.

Moreover, any arbitrary polarization that is transmitted through theoptical element 162 can be reduced to a weighted complex sum of firstand second orthogonal eigenpolarization components. The firstpolarization component corresponding to the slow eigenpolarization stateis slowed with respect to the second orthogonal polarization componentcorresponding to the fast polarization state on a first pass. In thesecond pass, the first polarization component is rotated so as tocorrespond to the fast eigenpolarization state and the secondpolarization component is rotated so as to correspond to the sloweigenpolarization state. The second polarization component is thereforeslowed with respect to the first polarization component by an equalamount on the second pass. The retardance of first polarizationcomponent introduced on the first pass is offset or compensated for bythe retardance of the second polarization component on the second pass.The retardance is said to be matched or balanced.

Thus, for a beam propagating from the central field point, theretardance contributed by the refractive element 162 on the second passis equal in magnitude but opposite in sign, orthogonal in orientation,to the retardance contributed by the refractive element 162 on the firstpass at all pupil coordinates (i.e., for all ray angles), resulting insubstantial cancellation of the retardance produced by the intrinsicbirefringence. For the exemplary embodiments discussed above inconnection with FIGS. 7A-7B, 8A-8B, and 9A-9B wherein the refractiveelement 162 is oriented respectively with its [111], [100], or [110]crystal axis aligned substantially parallel to the optical axis 165, andwith a 45° polarization rotator 180 located between refractive element162 and the reflecting element 164, the RMS retardance over the pupil isessentially zero for the central field point. For off-axis field points,the retardance aberrations from the first and second passes through therefractive element 162 are also substantially balanced, although thereare small residual retardance aberrations, since the beam followsdifferent paths through the refractive element 162 on the first andsecond passes. In the computer simulations conducted for these examples,the Faraday rotator 180 is assumed to be an ideal rotator with zerothickness.

For exemplary embodiments having refractive elements 162 oriented withits [111], [100], or [110] crystal axis aligned substantially in thedirection of the optical axis 165, and with a 45° non-reciprocal Faradayrotator 180 located so as rotate the polarization by about 90° in thefirst and second passes combined, the RMS retardance over the pupil is0.0006, 0.0001, and 0.0035 waves, respectively at a wavelength of 157.63nm. The respective peak-to-valley retardance is 0.0032, 0.0007, and0.0130 waves respectively. Peak-to-valley retardance is reduced byapproximately 128 times, 343 times, and 45 times, respectively byintroducing the rotator 180 into this Dyson design.

FIG. 11A is a graphical illustration of net retardance magnitude andorientation across the pupil for the extreme field point for theexemplary optical system 160 shown in FIG. 10 with refractive element162 having a [111] crystal axis aligned substantially along the opticalaxis 165. FIG. 11B is a graphical illustration of net retardancemagnitude and orientation across the pupil for the extreme field pointfor the exemplary optical system 160 shown in FIG. 10 with refractiveelement 162 oriented with its [110] crystal axis aligned substantiallyparallel to the optical axis 165. With a refractive element 162 having a[100] crystal axis substantially in the direction of the optical axis165, the retardance is very close to zero across the exit pupil, andthus, no retardance map has been provided.

Thus, by inserting a 45° Faraday rotator 180 between refractive element162 and reflective element 164 in the exemplary system 160 depicted inFIG. 10, each constituent polarization state is rotated by about 90°between the first and second passes through refractive element 162. Nearperfect correction of the retardance aberrations for the central fieldpoint is provided. Substantial balancing of retardance aberrations foroff-axis field points, with the refractive element 162 oriented with its[111], [100], or [110] crystal axis aligned substantially with theoptical axis 165 is also attained.

Faraday rotators are well known in the art. These devices will rotatethe polarization of light by a controllable amount. Other polarizationrotators may also be employed. These rotators may be active devices likethe Faraday rotator which rely on application of a magnetic field toinduce rotation of polarization states. Passive devices or combinationof active and passive devices are also possible.

An example of a 90° reciprocal wave plate rotator is constructed usingtwo quarter wave plates with their fast axes at 90° with respect to oneanother on either side of a half wave plate whose fast axis is at 45°with respect to the fast axes of the quarter wave plates; see, e.g., R.C. Jones, “A new calculus for the treatment of optical systems III: TheSohncke theory of optical activity,” J. Opt. Soc. Am., 31, p. 500-503,1941. These wave plates may be created using stress-inducedbirefringence (see, e.g., U.S. Pat. No. 6,084,708 issued to K. H.Schuster and U.S. Pat. No. 6,324,003 issued to G. Martin both of whichare incorporated herein by reference) or using uniaxial crystallinematerials. For a wave plate constructed by applying stress to a cubiccrystalline substrate, the stress birefringence coefficient is highestwhen the [100] crystal lattice direction is oriented along the systemoptical axis. The stress birefringence coefficient along the [100]direction is over 4 times larger than the coefficient along the [111]lattice direction [Alternative Materials Development (LITJ216) FinalReport—Stress Birefringence, Intrinsic Birefringence, and IndexProperties of 157 nm Refractive Materials, International SEMATECH, Feb.28, 2002, J. Burnett and R. Morton]. Thus, for a given plate thickness,the stress necessary to create a given retardance may be substantiallyreduced or minimized by orienting the wave plate with its [100] crystallattice direction along the optical axis, and cubic crystalline stresselements are often used with this orientation (see, e.g., U.S. Pat. No.6,201,634 issued to S. Sakuma which is incorporated herein byreference). Elements with weak retardance, other than the half waveplate, may also be placed between the quarter wave plates withoutsubstantially affecting the performance of the rotator. These type ofpolarization rotators will rotate any arbitrary polarization by 90°.

Other designs may be suitable in other cases. For example, if theincoming light has a known linear polarization, a quarter wave plate(QWP) can rotate polarization. On the first pass through the QWP,linearly polarized light may be converted into left circularly polarizedlight, if the QWP is at 45° to the polarization state. Reflection off amirror will transform the light into right handed circularly polarized.On the second pass through the QWP, the light is converted back intolinearly polarized light, with the polarization state rotated by 90°from that of the light initially incident on the QWP.

In other embodiments, the incoming and outgoing beams can be fullyseparated at the polarization rotator. A reciprocal or non-reciprocal90° polarization rotator may be inserted in the path of one of thebeams, in lieu of the 45° non-reciprocal rotator in both of the beams.Reciprocal rotators include, but are not limited to, wave plate rotatorsand rotators constructed using an optically active material with itsbirefringence axis oriented along the direction of the system opticalaxis. The optical configuration to provide a 90° polarization rotationis not limited to those described above, but may include otherpolarization rotators both well-known in the art and yet to be devised.

Example 2

A mixing rod, also referred to as a homogenizer or kaleidoscope, iscommonly used in illumination systems for photolithography. FIG. 12shows an exemplary mixing rod 200 comprising calcium fluoride and havingdimensions of 10×10×160 millimeters (mm). The mixing rod 200 is assumedto have a birefringence magnitude, n_(e)-n_(o), of −12×10⁻⁷,corresponding to the intrinsic birefringence of calcium fluoridemeasured at a wavelength of 157 nanometers (nm) as suggested in D.Krahmer, “Intrinsic Birefringence in CaF₂,” at Calcium FluorideBirefringence Workshop, Intl. SEMATECH, Jul. 31, 2001. The mixing rod200 has proximal and distal ends 202, 204 and an input and output facesor ports 206, 208 for inputting and outputting the beam and walls 210 onopposite sides for reflecting the beam propagating therethrough. Anoptical axis 212 extends the length of the mixing rod 200. The mixingrod 200 can be separated into two portions 214, 216, preferably of equallength, and more preferably having substantially the same retardance,i.e., the magnitude of retardance and the orientation of the retardanceaxis across the exit pupil is equivalent for both sections 214, 216. Thetwo sections 214, 216, come together at the axial center 218 of themixing rod 200.

A beam is input into the rod 200 by focusing it at the center of theinput port 206 of the mixing rod 200 along the optical axis 212. Thebeam may have, for example, a numerical aperture of about 0.5. The beampropagates from the input port 206 to the output port 208, raysreflecting from the sidewalls 210 within the mixing rod 200. Rays 220and 222 illustrate how light travels down the length of the rod 200.

FIG. 13 shows the net retardance across the exit pupil for a mixing rod200 comprising calcium fluoride having a [111] crystal axis in thedirection of the optical axis 212 of the mixing rod 200, assuming thatthe reflections from the walls 210 of the integrating rod 200 do notalter the polarization state of the light propagating therethrough. Inthese plots, the retardance orientation rotates by 90 degrees atone-half-wave (π or 180°) intervals, i.e., the effect of a 0.75 waveretarder at 0 degrees is the same as a 0.25 wave retarder at 90 degrees.Thus, the peak retardance due to intrinsic birefringence in this exampleis approximately 0.8 waves at a wavelength of 157 nanometers.

As discussed above, cubic crystal wherein the [111] crystal axis isaligned with the optical axis 212 of the optical element, here a mixingrod 200, is preferred. Cubic crystalline optical elements having anoptical axis along the [111] direction are easiest to grow with the lowstress birefringence levels that are required for lithographic qualityoptics, as the stress birefringence coefficient is minimized along the[111] axis (see, e.g., U.S. Pat. No. 6,201,634 issued to S. Sakuma).While the [111] orientation is preferred, the reduction of retardanceaberrations can achieved using the techniques described herein for othercrystal orientations as well.

FIG. 14 shows the polarization state across the exit pupil when auniformly circularly polarized beam is incident on the entrance face ofthe mixing rod 200. The output polarization state is not uniformlypolarized as a result of retardance. Uniform polarization, however, isdesirable for illumination of the reticle in photolithographyapplications, and without compensation, this mixing rod 200 will produceunacceptable reticle dependent distortion and linewidth variations.

In FIG. 14, and the polarization state pupil maps to follow, thepolarization state of the beam is shown on a square grid across thesystem exit pupil for the optical system of interest and is described ingeneral by ellipses which sometimes degenerate into lines. The shape andorientation of the ellipse or line at a given pupil coordinate depictthe state and orientation of the output polarization state at the exitpupil.

FIG. 15 is a schematic side view of the mixing rod 200 furthercomprising polarization rotation optics 230 disposed at the axial center218 of the mixing rod 200. Preferably, the polarization rotation optics230 is a 90° rotator that rotates the polarization by about 90°. Thepolarization transforming optics 230 may be a reciprocal ornon-reciprocal rotator. This rotator 230 is preferably positioned withinthe mixing rod 200 at the location 218 between the two sections 214,216, which each preferably introduce equivalent retardance, i.e., bothin magnitude and orientation. The rotator 230 is thus inserted betweensections 214, 216 having matched birefringence and retardanceproperties.

In one exemplary embodiment, a stress birefringence wave plate rotatoris employed, although other types of polarization rotation optics mayalso be used. As discussed above, a wave plate rotator may beconstructed using two quarter wave plates with their fast axes at 90°with respect to one another on either side of a half wave plate whosefast axis is at 45° with respect to the fast axes of the quarter waveplates; see, e.g., U.S. Pat. No. 6,084,708 issued to K. H. Schuster andU.S. Pat. No. 6,324,003 issued to G. Martin, both of which areincorporated herein by reference in their entirety. In one embodiment,the half-wave plate comprises a 2 millimeter thick [100] calciumfluoride element and the quarter waveplates each comprise a 1 millimeterthick [100] calcium fluoride elements. The [100] orientation isadvantageous because of the higher amount of birefringence in comparisonwith other orientations like the [111] and [110].

On-axis, the 90° rotator 230 produces a rotation of each constituentinput polarization state of approximately 90° or π/4 radians. Theeigenpolarization states of a rotator are circularly polarized and the90° rotator exhibits 90° of phase delay between the two orthogonallypolarized circular states, or a quarter-wave of circular retardance. Foroff-axis rays, the retardance of the wave plates deviates from theiron-axis values due to the variation of refractive index with angle aswell as the change in the optical path through the waveplates. Thus, therotator 230 will deviate from a quarter wave of circular retardance foroff-axis rays. FIG. 16 shows the magnitude of the retardance error as afunction of angle of incidence in air for 1 and 3 millimeter thickquarter wave plates (curves 232 and 234 respectively) for a wavelengthof 157 nm. The index differences between the two orthogonal polarizationstates are 3.9×10⁻⁵ and 1.3×10⁻⁵ for curves 232 and 234, respectively,as indicated in the legend. Over a 30° angle of incidence range in air,the retardance error is within approximately 0.03 waves, which isacceptable for many illumination applications.

The polarization rotation optics 230 allows the retardance to be reducedfor all polarization states, i.e., for any arbitrary polarization or forunpolarized light, both which comprise a weighted sum of orthogonalpolarization states. For example, the polarization state of lightentering the mixing rod 200 at the input 202 can be separated into theorthogonal eigenpolarization states associated with each of the firstand second sections, 214, 216. Since the two sections are substantiallyidentical, the eigenpolarizations of the two sections 214, 216 are thesame. This characteristic can be exploited to compensate or offset theretardance introduced by each of the sections 214, 216.

In particular, light input into the mixing rod 200 will have first andsecond orthogonal polarization components corresponding to the slow andfast eigenpolarizations of the first section 214 of the mixing rod 200,respectively. The first polarization component will thus be retardedwith respect to the second polarization component by an amountcorresponding to the retardance introduced by the first section 214 ofthe mixing rod 200. This light will pass through the polarizationrotation optics 230, which will rotate the polarization components 90°such that the first polarization component will correspond to the fasteigenpolarization of the second section 216 and the second polarizationwill correspond to the slow eigenpolarization of the second section 214.The second polarization component will thus be retarded with respect tothe first polarization component by an amount corresponding to theretardance introduced by the second section 216 of the mixing rod 200.Since the birefringence of the first and second sections 214 and 216 aresubstantially the same, the birefringent and retardance properties ofthe two sections 214 and 216 being matched, the retardance encounteredby the first and second components upon passing through the first andsecond sections 214, 216 will be offset. The first component is retardedby an equal amount in the first section as the second component isretarded in the second section. The retardance contributed by the firsthalf 214 of the mixing rod 200 being substantially equal in magnitudebut nearly orthogonal in orientation to the retardance contributed bythe second half 216 of the mixing rod 200 at all pupil coordinates(i.e., for all ray angles), results in substantial cancellation of theretardance produced by the intrinsic birefringence.

FIG. 17 shows the net retardance across the exit pupil of the exemplaryembodiment shown in FIG. 15. The peak retardance due to intrinsicbirefringence in this example is less than 0.044 waves peak-to-valley ata wavelength of 157 nanometers, which is substantially reduced from thepeak-to-valley retardance of 0.8 waves before the rotator was added.

FIG. 18 shows the polarization state across the exit pupil when auniformly circularly polarized beam is incident on the entrance face 206of the mixing rod 200 shown in FIG. 15 which includes the polarizationrotation optics230. The output polarization state is substantially moreuniform, i.e., circularly polarized, than the output polarization forthe mixing rod 200 without the rotator 230 depicted in FIG. 12, and isthus more suitable for photolithography.

Example 3

These techniques for reducing polarization aberrations caused byintrinsic birefringence are particularly well suited for providingwavefront correction of refractive imaging systems used forphotolithography. In addition to the rigorous performance requirementsassociated with this application, photolithography lenses often includea large number of refractive optical elements, which together possess asignificant amount of birefringence. Wavefront error caused byretardation aberrations can therefore substantially limit the resultantresolution obtained by the photolithographic projection system. Anexemplary projection lens 100, one which contains all opticallytransmissive and, in particular, all refractive, powered, opticalelements L1-L29 is illustrated in FIG. 1. A similar lens is provided inEuropean Patent Application No. 0 828 172 by S. Kudo and Y. Suenaga, thecontents of which are herein incorporated by reference. This opticalsystem 100 is designed to operate at a central wavelength of 193.3nanometers, provides a 4× reduction at a numerical aperture of 0.60, andhas an image field diameter of 30.6 millimeters (mm). The exemplarydesign employs twenty-nine (29) optical elements L1-L29 comprisingcalcium fluoride and fused silica and uses only spherical surfaces.Retardation aberrations, however, are calculated below for a similarlens having the same prescription as disclosed in European PatentApplication No. 0 828 172 but with all the lens comprising cubiccrystalline material, namely calcium fluoride. Accordingly, eachcomponent L1-L29 is assumed to have an intrinsic birefringence of−12×10⁻⁷ in these baseline computations. The actual value of intrinsicbirefringence may vary depending on the material or in the case wherethe material is crystal, the crystal orientation. Also, in otherembodiments, one or more of the optical elements L1-L29 may comprisecrystalline material other than cubic crystals as well asnon-crystalline materials. Fused silica is an example of such anon-crystalline material that is substantially optically transmissive toUV wavelengths such as 248 nm and 193.3 nm and is therefore compatiblewith such UV applications. As discussed above, the exemplary system 100includes an optical axis 106, the twenty-nine (29) optical elementsL1-L29 being aligned along this optical axis 106 as is customary for onaxis optical systems. An optical beam propagates along the optical axis106, from the object plane 106 to the image plane 104 through the lenselements L1-L29 in the lens 100.

The RMS and maximum retardance and diattenuation over the exit pupil arelisted in Table 2 below for the nominal design without intrinsicbirefringence effects included for relative field heights of 0, 0.7, and1.0. As described above, diattenuation, another form of polarizationaberration, is a measure of the maximum difference in transmissionbetween orthogonal polarization states. The relative field height isdefined to be the actual field height normalized by the semi-fieldheight. Thus, an image located on the optical axis 106 has zero fieldheight and an image located at 15.30 mm in this lens 100 corresponds tounit relative field height. The retardance and diattenuation result fromthe single-layer anti-reflection coatings used in the model. Theretardance is radially oriented and is largest in magnitude at the edgeof the pupil. The retardance due only to the anti-reflective coating isrelatively small.

TABLE 2 Relative Retardance Field (waves at λ_(o) = 193.3 nm)Diattenuation Height RMS Maximum RMS Maximum 0.0 0.0021 0.0077 0.00190.0076 0.7 0.0024 0.0086 0.0023 0.0091 1.0 0.0028 0.0111 0.0031 0.0127

When the effects of intrinsic birefringence associated with the cubiccrystalline lens material are taken into account, system performancedegrades significantly. FIGS. 19A and 19B are graphical illustrationsshowing the net retardance across the system exit pupil for field pointsat the center and edge of the field, respectively, according to anexemplary embodiment in which all lens elements L1-L29, shown in FIG. 1,are identically aligned in three dimensions, with the elements havingtheir [110] crystal axis direction along the optical axis 106. FIGS. 19Aand 19B include the effects of intrinsic birefringence. FIG. 19A showsthe net retardance at various positions across the exit pupil for a beamof light originating from a point in the object field location in FIG.19A which is 0 mm away from the optical axis 106. FIG. 19B quantifiesthe net retardance at various locations across the exit pupil for a beamof light originating from a point in the object field at a height is61.2 mm away from the optical axis 106. These two points correspond tothe center and edge field points, respectively. This edge field pointmay, for example, map into a point at the edge of the frame of aphotolithography instrument for processing semiconductor wafers. In theretardance pupil maps given in FIGS. 19A and 19B, and in others tofollow in which the net retardance exceeds a magnitude of 0.5 waves, theretardance is plotted “modulo 1 wave.” It can therefore be seen that theretardance orientation rotates by 90 degrees at one-half-wave (π radiansor 180°) intervals, i.e., the effect of a 0.75 wave retarder at 0degrees is the same as a 0.25 wave retarder at 90 degrees. Thus, thepeak retardance due to intrinsic birefringence in this exemplaryarrangement is approximately 0.72 waves at a wavelength of 193.3nanometers on axis and 0.87 waves at the extreme field.

FIGS. 20A and 20B are graphical illustrations of the retardance foranother exemplary embodiment of crystal lattice orientation of the lenssystem 100 shown in FIG. 1. In FIGS. 20A and 20B, the net retardanceacross the system exit pupil, including the effects of intrinsicbirefringence, is depicted for field points at the center and edge ofthe field 102 with the crystal axes of all the elements L1-L29substantially identically aligned, with the [100] crystal axes generallydirected parallel to the optical axis 100. The peak retardance due tointrinsic birefringence in this example is approximately 0.49 waves at awavelength of 193.3 nanometers on-axis and 0.54 waves at the extremefield.

FIGS. 21A and 21B are graphical illustrations of the retardance of yetanother exemplary embodiment of crystal lattice orientation of the lenssystem 100 shown in FIG. 1. In FIGS. 21A and 21B, the net retardanceacross the system exit pupil is depicted for field points at the centerand edge of the field 102 with the crystal axes of all elements L1-L2substantially identically aligned, for [111] optical elements, i.e.,elements comprising [111] crystal with the [111] direction parallel tothe optical axis 106. Again, the retardance orientation rotates by 90degrees at one-half-wave (π radians or 180°) intervals; thus, the peakretardance due to intrinsic birefringence is approximately 1.37 waves ata wavelength of 193.3 nanometers, and 1.40 waves at the extreme field.

In these three preceding examples, as illustrated in FIGS. 19A-21B, theintrinsic birefringence produces large retardance aberrations andconsequently large wavefront aberrations, when each of the elementsL1-L29 are oriented identically with respect to the optical axis 106.Without compensation, this wavefront aberration strongly exceeds theallowable wavefront error for high precision photolithography.

To reduce this aberration, two polarization rotators are added to theoptical system 100 to compensate the retardance produced by theintrinsic birefringence of the optical elements L1-L29. See FIG. 22,which shows a similar lens 300 as presented in FIG. 1, but with twopolarization rotators 310 and 320 which rotate the polarization of abeam of light passing therethrough by −90° and 90° respectively. Thislens 300 has an optical axis 302, which defines an optical path for abeam of light to propagate from an object plane 306 to an image plane308. The optical path follows a straight line in FIG. 22, however, inother embodiments, the optical path and the optical axis 302 may beother than straight and linear. The lens 300 comprises twenty-ninepowered refractive optical elements L1-L29 that transmit and control thepropagation of light from the object 306 to the image field 308.

In FIG. 22, the −90° rotator 320, which is optional, is located betweenthe object plane 306 and the first element L1. The 90° rotator 310 ispositioned at the location that minimizes the net system retardancewithout additional changes to the operation of the system 300. Thisposition is preferably determined such that the birefringence of theoptical element(s) L1-L26 in the portion of the optical path precedingthe rotator 310 is equivalent to the birefringence of the opticalelement(s) L27-L29 in the optical path following the rotator 310.Similarly, the net retardance introduced by the optical elements L1-L26,L27-L29 in the path before and after the rotator 310 are matched andbalance. Both the magnitude of the retardance and the orientation or theretardance axis substantially the same. Expressed yet another way, theeigenpolarizations states corresponding to the optical element orelements L1-L26 through which light passes prior to reaching the rotator310 are preferably substantially identical to the eigenpolarizationstates corresponding to the optical element or elements, L27-L29 throughwhich light passes after the rotator 310.

In calculating the improved performance of the lens 300, the rotators310 and 320 are assumed to be ideal polarization rotators, such thateach constituent polarization state is rotated by exactly 90 or −90°.Additionally, these rotators 310 and 320 are assumed to have zerothickness. The lens prescription may be adjusted and optimized forfinite thickness rotators 310 and 320 as well. The optical axis 302 isdefined along the Z direction, the field is oriented in the Y direction,and a right handed coordinate system is used; thus, a 90° rotation aboutthe optical axis 302 represents a rotation of the X axis towards the Yaxis. The order of the rotators 310, 320 may be switched withoutchanging the performance, such that a 90° rotator 310 is used in objectspace, and a −90° rotator 320 is used between elements L26 and L27.Also, the rotator 320 in object space may, in principle, bealternatively used in image space (between the last element L29 and theimage plane 308). However, for this particular design, as well as manyphotolithography lenses, the performance of a real rotator may be betterif it is located in object space, since the range of incident angles islower. Having some rays incident on the rotator 310, especially onecomprising waveplates, at a high angles causes variations in the phasedelay and thus not all rays experience the same polarization rotation.Preferably, the rotator 310 is positioned where the rays propagatethrough the optical system 300 are more closely parallel to the opticalaxis 302 and not substantially angled with respect thereto. Preferably,the polarization is rotated substantially uniformly across the beam oflight that passes through the rotator 310. For rays substantially alongor parallel to the optical axis, the retardance and phase shift is thesame. Thus, at least rays having small angle with respect to the opticalaxis 302, will undergo substantially that same amount of polarizationrotation.

Substantial benefit is obtained by inserting the 90° polarizationrotator 310 between front and rear parts 322 and 324 of the lens 300. Asdiscussed above, the location of the rotator 310 is chosen such that thenet retardance produced by the cubic crystalline elements in the frontpart 322 of the system 300 are similar in magnitude as a function offield and pupil position to the net retardance produced by the cubiccrystalline elements in the rear part 324 of the system 300. The rotator310 allows the retardance contributions of the individual elementsL1-L29 to be balanced to provide wavefront correction and reduce the netretardance produced by the intrinsic birefringence to an acceptablelevel. Under these conditions, the system 300 will have a uniformcircular retardance of 90 degrees. The 90 degrees of circular retardancewill rotate an arbitrary polarization state by 90 degrees. The lightinput into the optical system 300 will experience minimal wavefrontaberrations, although the polarization state will be rotated by 90degrees between the object and image planes 306 and 308, because of the90° of circular retardance.

In order to evaluate the magnitude of the deviation of the retardancefrom 90 degrees, the −90 degree rotator 320, is inserted between theobject 306 and first lens element L1. This second rotator 320 is used inthis example as a computational aid and may or may not be included inthe optical system 300. This second rotator 320 may be included inoptical systems 300, for example, if the input and output polarizationsneed to be identical. Insertion of the second rotator 320 into the lensmodel also facilitates optimization of the system 300 by allowing thedesigner to simply optimize the retardance aberrations using a meritfunction that only contains the magnitude of the retardance. In thiscase, the designer just needs to reduce the magnitude of the retardanceto zero. Without the second rotator, the designer would need to optimizeon the magnitude and shape of the retardance to be constant across thepupil. This merit function would have twice as many terms and would takelonger to optimize. An additional rotator 320, however, may introduceadditional complexity and cost into the optical system 300 and thus maybe excluded.

All the optical elements L1-L29 in the optical system 300 depicted inFIG. 22 comprise cubic crystalline material oriented with identicalthree-dimensional crystal lattice directions and with the [100] crystallattice direction for each element L1-L29 along the system optical axis302. Additionally, each of these optical elements comprise curvedsurfaces and are powered refractive optical elements. Operation is at awavelength, 193.3 nanometers, where each optical element L1-L29 issubstantially optically transmissive.

FIGS. 23A and 23B are graphical representations that depict theretardance across the system exit pupil for optical elements L1-L26 inthe front portion 322 of the system 300, between the −90° and 90°rotators 310 and 320. The retardance is caused by the intrinsicbirefringence and anti-reflection coatings. As previously shown in Table2, the contribution due the coatings is relatively small; thus, the bulkof the retardance aberration is due to the intrinsic birefringence. FIG.23A shows net retardance at the center field point and FIG. 23B showsnet retardance at the edge field point.

FIGS. 24A and 24B are graphical representations that depict theretardance across the system exit pupil for optical elements L27-29 inthe rear portion 324 of the system 300, between the 90° rotator 310 andthe image plane 308. FIG. 24A shows net retardance for the center fieldpoint and FIG. 24B shows net retardance for the edge field point.

Comparing FIGS. 23A and 24A, the net retardance from the front portion322 of the system 300 is substantially similar to the net retardancefrom the rear portion 324 of the system 300 across the pupil for thebeam emanating from the axial field point. Thus, because the 90° rotator320 rotates each constituent polarization state by 90°, the retardanceof the rear portion 324 of the system 300 will compensate the retardanceof the front portion 322 of the system 300. The slow eigenpolarizationstates of the two portions 322 and 324, which are shown in FIGS. 23A and24A, respectively, are linear across the exit pupil. Thus, in this case,light propagating through the first portion 322 having a firstpolarization component parallel to the slow eigenpolarization state ofthe first portion 322 is retarded with respect to a second orthogonalpolarization component that is parallel to the fast eigenpolarizationstate. The phase of the first polarization is retarded with respect tothat of the second polarization by an amount corresponding to theretardance introduced by the first portion 322. The polarization rotator320, however, rotates the polarization of the first and secondpolarization components such that the first polarization component isparallel to the fast eigenpolarization state in the second portion 324and the second polarization state is parallel to the sloweigenpolarization state. The second polarization component is thereforeretarded with respect to the first polarization component in the secondportion 324 by an amount equal to the retardance introduced to the firstpolarization in the first portion 322. The retardances thus cancel.

FIGS. 23B and 24B show that the net retardance across the pupil for thefront and rear portions 322 and 324 of the optical system 300 are not aswell matched at the extreme field. The retardance contribution of thefront portion 322 is larger in magnitude and is not centered in thepupil.

FIGS. 25A and 25B are graphical representations that depict the netretardance across the system exit pupil due to intrinsic birefringenceof all elements L1-L29, including the 90° rotator 310, but excluding the−90° rotator 320. These plots show that the rotator 310 contributes aroughly constant retardance across the pupil that can be balanced withthe retardance produced by a second rotator 320. In general, to reduceaberration, an optical system preferably has no variation in thepolarization state across the pupil. This occurs when the retardance isconstant or degenerately when there is no retardance. In the degeneratecase, any polarization state is an eigenpolarization state.

FIGS. 26A and 26B are graphical representations that depict the netretardance across the system exit pupil due to intrinsic birefringenceof all elements L1-L29, including the 90° and −90° rotators 310 and 320.The retardance introduced by the 90° rotator 320 is offset by theretardance introduced by the −90° rotator 320 for further correction. Asshown, the net retardance for the axial field has been significantlyreduced compared with the retardance for all the [100] elements L1-L29without rotators 310, 320 shown in FIG. 20A. FIG. 26B, however, showslarger residual retardance across the pupil.

The RMS and maximum retardance over the exit pupil are listed in Table 3below for relative field heights of 0, 0.7, and 1.0. These include theeffects of intrinsic birefringence and the single layer anti-reflectioncoatings used in the model. A relative field height of 0.0 correspondsto the center field point is associated with the retardance resultsshown graphically in FIG. 26A, and a relative field height of 1.0corresponds to the edge field point, retardance results of which areshown graphically in FIG. 26B. The RMS retardance ranges from 0.0154 to0.0677 waves at λ_(o)=193.3 nm.

TABLE 3 Retardance (waves at λ_(o) = 193.3 nm) Relative Field Height RMSMaximum 0.0 0.0154 0.0606 0.7 0.0528 0.2486 1.0 0.0677 0.3826

Further correction may be achieved by applying stress to one or moreelements to produce stress induced birefringence. For example, a clamp,brace, or other structure around a perimeter of an optical component canbe employed to apply, e.g., tensile or compressive forces to the opticalcomponent. In the one embodiment depicted in FIG. 27, a tensile hoopstress was applied to the first element L1 of the optical system 300depicted in FIG. 22. For purposes of calculations, the tensile hoopstress is assumed to produce a radial variation in birefringence with apeak birefringence magnitude of −6.95 nanometers/centimeter at the clearaperture diameter. FIG. 28A shows a contour plot of the assumedbirefringence profile. FIGS. 28B and 28C are graphical representationsthat depict the retardance across the system exit pupil due to stressinduced intrinsic birefringence and anti-reflection coatings associatedwith the first lens element L1. Table 4 lists the corresponding RMS andmaximum retardance values as a function of relative field height. Thisdata shows that there is a relatively small contribution on axis 302,with a peak retardance of 0.025 waves at λ=193.3 nm, while theretardance at the extreme field is much larger, with a maximumretardance of 0.31 waves.

The first element L1 in this design is particularly well suited forapplication of hoop stress to introduce birefringence. The first elementL1 can provide a large variation in retardance with field since it isclose to the object plane 306 thereby resulting in variation indisplacement of the beam across the surface of the first element L1 withdifferent field heights. Also, this element L1 in this example isparticularly thick, which provides good mechanical stability forapplying stress to the element.

TABLE 4 Retardance (waves at λ_(o) = 193.3 nm) Relative Field Height RMSMaximum 0.0 0.0070 0.0252 0.7 0.0383 0.1856 1.0 0.0505 0.3134

Comparing FIGS. 28B and 28C with the residual retardance maps given inFIGS. 26A and 26B, the retardance produced by the stress inducedbirefringence is substantially similar to the residual system retardanceas a function of pupil and field position. Because a 90° rotator 310 isused following the element L1 with stress induced birefringence, theretardance contribution of the stressed element L1 balances the netretardance of the system 300 resulting from intrinsic birefringence.

FIGS. 29A and 29B are graphical representations that depict the netretardance across the system exit pupil due to intrinsic birefringenceof all elements L1-L29, including the 90° and −90° rotators 310 and 320and the stress induced birefringence on the first element L1.Corresponding values for RMS and maximum retardance are listed in Table5. As shown, the retardance produced by the stressed element L1 furtherimproves the retardance correction.

TABLE 5 Retardance (waves at λ_(o) = 193.3 nm) Relative Field Height RMSMaximum 0.0 0.0127 0.0517 0.7 0.0146 0.0722 1.0 0.0161 0.0811

The retardance using all [100] elements without rotators 310 and 320 isshown in FIGS. 20A and 20B. With the two rotators 310 and 320 and thestressed first element L1, the maximum retardance was reduced from 0.488waves to 0.0517 waves at X=193.3 rim for the axial field (9.4×reduction) and a reduction in maximum retardance from 0.544 waves to0.0811 waves at the extreme field (6.7× reduction).

In this example, the application of hoop stress to an optical element L1was assumed to produce a quadratic variation in the magnitude of thebirefringence, with the birefringence axis oriented radially. In FIG.30, the retardance as a function of element radius calculated usingfinite element analysis methods is shown for a meniscus shaped calciumfluoride element with 5 mm center thickness, radii of curvature of 40and 35 mm, and a compressive stress of 1000 pounds per square inch. Thefracture strength of a well-polished single crystal of calcium fluoridehas been reported to be in excess of 20,000 pounds per square inch.Although this first lens element L1 differs from the meniscus shapedelement, the variation in stress is expected to follow a similarfunctional form. In alternative embodiments, tensile stress, may beemployed to create stress-induced birefringence.

As is commonly known in the art and shown in FIG. 31A, a realpolarization rotator 350 for rotating polarization direction may beconstructed using two quarter wave plates 354 and 356 and a half waveplate 358 aligned along a common optical axis 352. The two quarter waveplates 354 and 356 have fast axes 360 and 362 rotated about the opticaxis 352 by 90° with respect to one another. The half wave plate 358 isinserted between the two quarter wave plates 354 and 356 and has a fastaxis 364 at an angle of about 45° with respect to the fast axes 360 and362 of the quarter wave plates 354 and 356. This rotator 350 willconvert any arbitrary polarization state into a new polarization statecorresponding to the old state with the polarization orientation rotatedby 90°. Such a polarization rotator is described in see, e.g., U.S. Pat.No. 6,084,708 issued to K. H. Schuster and U.S. Pat. No. 6,324,003issued to G. Martin, both of which are incorporated herein by referencein their entirety.

Elements (not shown) with weak retardance, other than the half waveplate 356, may also be placed between the quarter wave plates 354 and356 without substantially affecting the performance of the rotator 350.These additional elements may, for example, include powered opticalelements. These wave plates 354, 356, and 358 may be created usingstress induced birefringence or using uniaxial materials. For awaveplate constructed by applying stress to a cubic crystallinesubstrate, the stress birefringence coefficient is highest when the[100] crystal lattice direction is oriented along the system opticalaxis 352. The stress birefringence coefficient along the [100] directionis over 4 times larger than the coefficient along the [111] latticedirection. Thus, for a given plate thickness, the stress necessary tocreate a given retardance may be minimized by orienting the wave platewith its [100] crystal lattice direction along the optical axis 352, andcubic crystalline stress elements are often used with this orientation.See for example, U.S. Pat. No. 6,201,634 issued to S. Sakuma, et al.,and U.S. Pat. No. 6,324,003 issued to G. Martin, which are incorporatedherein by reference.

A real quarter wave plate has a residual retardance error that dependson numerical aperture and birefringence magnitude. In FIG. 31B, theestimated residual retardance error is plotted over a numerical aperturerange of 0.0 to 0.5 and a range of intrinsic birefringence from 1×10⁻⁶to 1×10⁻⁴. Over these ranges, the residual retardance error is less than⅛^(th) wave; these results suggest that the performance for realrotators constructed from wave plates should be acceptable forcompensation in many applications such as for lithography lenses.

Other types of polarization rotators 350 different than that shown inFIG. 31A may alternatively be employed. These include, but are notlimited to, Faraday rotators and rotators constructed using an opticallyactive material such as crystal quartz or sugar water. When making aquartz rotator, the material is cut so that the birefringence axis isparallel to the optical axis, whereas the birefringence axis isperpendicular to the optical axis in quartz linear retarders.

In addition, although the polarization rotator 350 shown in FIG. 31Arotates the polarization by 90 degrees, compensation and reduction inpolarization aberrations can be provided if odd integer multiples of 90degrees (i.e., ±90, ±270, etc.) are provided as well. For example, apolarization rotator that rotates an arbitrary polarization by ±270about the direction of propagation may be situated between two portions322, 324 of the optical system 300 having equivalent birefringence.

Also, although 90° of rotation is introduced at one location along theaxis 302 of the optical system 300, the optical system 300 is not solimited. In other designs, an odd number of 90° of rotators may be used.For example, three polarization rotators each rotating the polarizationby 90° may be inserted in three locations within the optical system 300.Preferably, these three 90° polarization rotators would separate theoptical system into four portions. The locations would preferably beselected such that the birefringence from each of the four portionswould substantially cancel out. In other designs, the polarization canbe rotated by amounts other than 90°. Specifically, if there is an oddnumber of rotators, n, the rotation of each rotator can be 180°/(n+1).For example, three polarization rotators each rotating the polarizationby 45° may be inserted in three locations within the optical system 300.Preferably, these three 45° polarization rotators would separate theoptical system into four portions. The locations would preferably beselected such that the birefringence from each of the four portionswould substantially cancel out. There are many possible ways to userotators to cancel the intrinsic birefringence and these examples aremerely illustrative and not restrictive. It is expected that the singlerotator solution will usually be the very cost effective, because it isthe simple.

Also, although non-powered waveplates 354, 356, and 358, are shown asforming the polarization rotator 350, the waveplate (and/or rotator)functions may be integrated with lens functions in other designs. Thewaveplates 354, 356, and 358 may, for example, contain curved surfacesand thus possess power, which contributes to the operation of theoptical system 300. Such integration may increase the complexity of thedesign but also provides additional possibilities. Accordingly,polarization rotation elements which contain power are consideredpossible.

Also, rotations other than 90° may be desired when the birefringence oftwo portions 322, 324 of the optical system to not completely match butare rotated with respect to each other. For example, if thebirefringence in first and second portions 322, 324 of the opticalsystem 300 have birefringence rotated about 10° with respect to eachother, a 100° polarization rotator, may be inserted between the twoportions 322, 324 to provide for compensation and cancel out theretardance contributed by the two portions 322, 324.

Example 4

Another exemplary all-refractive projection lens 400 comprising poweredrefractive optical elements is depicted in FIG. 32. Such an exemplaryimaging lens 400 may be used for photolithography and, in particular,may be used in the semiconductor manufacturing industry. A similar lensdisclosed in European Patent No. 1 139 138 A1 issued to Y. Ohmura isdesigned to operate at a central wavelength of 193.3 nanometers,provides 4× reduction at a numerical aperture of 0.75, and has an imagefield diameter of 27.5 mm. The design employs twenty-eight opticalelements L1-L28 aligned on an optical axis 402, each lens element L1-L28being constructed from calcium fluoride and fused silica. Three of thesurface on the optical elements L1-L28 are aspheric. These opticalelements L1-L28 are substantially optically transmissive to UV light.The lens 400 depicted in FIG. 32 possesses substantially the same lensprescription as that disclosed in European Patent No. 1 139 138 A1except that all the lens elements L1-L28 in lens 400 of FIG. 32 comprisecalcium fluoride and are assumed to have an intrinsic birefringence of−12×10⁻⁷ for purposes of calculations. In other embodiments, however,some of the lens elements L1-L28 may be formed of non-cubic crystallinematerial or additional lens elements or other optically transmissiveelements may be formed of non-cubic crystalline material. Varioussuitable non-cubic crystalline materials such as dry fused silica may beused, for example.

FIG. 32 shows the imaging lens 400 with object plane 404, which may be,e.g., a reticle or photomask, image plane 406, which may be, forexample, a substrate upon which the image is formed, and aperture stop,AS, 408.

RMS and maximum retardance and diattenuation over the exit pupil arelisted in Table 6 for the nominal design without intrinsic birefringenceeffects included for relative field heights of 0, 0.7, and 1.0. Theretardance and diattenuation result from the single-layeranti-reflection coatings used in the model. The retardance is radiallyoriented and is largest in magnitude at the edge of the pupil.

TABLE 6 Retardance (waves Relative Field at λ_(o) = 193.3 nm)Diattenuation Height RMS Maximum RMS Maximum 0.0 0.0048 0.0177 0.00680.0273 0.7 0.0049 0.0184 0.0069 0.0274 1.0 0.0053 0.0216 0.0075 0.0310

Table 7 shows RMS and peak-to-valley wavefront error for the nominaldesign, without the effects of intrinsic birefringence. Wavefront errorsare given for relative field heights of 0, 0.7, and 1.0 in the Ydirection, and are listed for two orthogonal polarization components.The X component represents the wavefront error for an input polarizationin the X direction assuming a linear polarizer along the X direction atthe system exit pupil. The Y component represents the wavefront errorfor an input polarization in the Y direction assuming a linear polarizeralong the Y direction at the exit pupil. Without cubic crystallineoptical elements, or the effect of intrinsic birefringence considered,the nominal design includes a peak RMS wavefront error of 0.004 waves.

TABLE 7 RMS Wavefront Error Peak-to-Valley (waves at Wavefront Errorλ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) Relative Field X Y X YHeight Component Component Component Component 0.0 0.003 0.003 0.0170.017 0.7 0.003 0.004 0.022 0.033 1.0 0.003 0.004 0.022 0.029

FIGS. 33A, 33B, 33C, and 33D show wavefront errors plotted at the systemexit pupil as contour maps for the nominal design without intrinsicbirefringence effects included. FIGS. 33A and 33B show contour plots ofthe residual wavefront error for the exemplary lens 400 depicted in FIG.32 corresponding to an input polarization in the X direction,perpendicular to the field height, used with an exit pupil analyzer inthe X direction for the center and extreme field points, respectively.For the wavefront error at the central field point, the maximumpeak-to-valley optical path difference is 0.017 waves at a wavelength of193.3 nanometers, and for the wavefront error at the extreme field, themaximum peak-to-valley optical path difference is 0.022 waves. FIGS. 33Cand 33D show contour plots of the residual wavefront error for the lensdepicted in FIG. 32 corresponding to an input polarization in the Ydirection, parallel to the field height, used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the wavefront error at the central field point, themaximum peak-to-valley optical path difference is 0.017 waves at awavelength of 193.3 nanometers, and for the wavefront error at theextreme field, the maximum peak-to-valley optical path difference is0.029 waves.

Table 8 shows the distortion for the nominal design, calculated based oncentroid of the point spread function, and the telecentricity error inthe Y direction at relative field heights of 0, 0.7, and 1.0. Distortionis the deviation of the image location from the ideal position.Distortion is preferably reduced or minimized in lithography systems, sothat features printed on one layer of an integrated circuit areprecisely registered with the other layers which are potentiallyfabricated using a different lithography tool. Because the distortionmust be controlled even when the object and image are not perfectlyfocused, the cones of light must be normal to the object and image.Otherwise, the image centroids will deviate depending on the focusposition (i.e. focus dependent distortion). Deviations from normalincidence of the image cones are known as telecentricity errors.

TABLE 8 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.00 7.70 0.11 1.0 0.00 10.70 0.51

When each of the optical elements L1-L28 in the lens 400 depicted inFIG. 32 comprises cubic crystalline material exhibiting intrinsicbirefringence in FIG. 32, the optical performance degradessignificantly. FIGS. 34A and 34B show the net retardance across thesystem exit pupil for field points at the center and edge of the field(at object field heights of 0 and 55 mm) according to an exemplaryembodiment in which all elements L1-L28 comprise cubic crystalsubstantially identically aligned in three dimensions, with the [110]crystal axis directed along optical axis 402. In these plots, theretardance orientation rotates by 90 degrees at one-half-wave (π radiansor 90°) intervals, i.e., the effect of a 0.75 wave retarder at 0 degreesis the same as a 0.25 wave retarder at 90 degrees. Thus, the peakretardance due to intrinsic birefringence in this example isapproximately 2.1 waves at a wavelength of 193.3 nanometers.

FIGS. 35A and 35B show the net retardance across the system exit pupilfor field points at the center and edge of the field 404, respectively,according to another exemplary arrangement in which all elements areidentically aligned in three dimensions, with the elements' L1-L28 [100]crystal axes direction parallel to optical axis 402. Again, theretardance orientation rotates by 90 degrees at one-half-wave intervals;thus, the peak retardance due to intrinsic birefringence in this exampleis approximately 1.5 waves at a wavelength of 193.3 nanometers.

FIGS. 36A and 36B show the net retardance across the system exit pupilfor field points at the center and edge of the field 404, respectively,according to another exemplary arrangement in which all elements arealigned identically in three dimensions, with the respective [111]crystal axes of the different optical elements directed along opticalaxis 402. In this exemplary arrangement, the peak retardance due tointrinsic birefringence is approximately 0.8 waves at a wavelength of193.3 nanometers.

With the crystal axes of each of the optical elements L1-L28 orientedidentically in three dimensions, the retardance produced by intrinsicbirefringence produces large wavefront aberration. Without compensation,this aberration strongly exceeds the desirable wavefront error requiredfor photolithography processes, particularly for photolithographyprocesses used to produce the small feature sizes in today'ssemiconductor manufacturing industry.

To reduce retardance aberration at least one polarization converter 410in inserted in the optical system 400 as illustrated in FIG. 37. Thepolarization converter 410 comprises a 90° polarization rotator, whichis placed in the optical system 400 thereby dividing the system intofirst and second (front and rear) groups 412 and 414. The net retardanceproduced by the cubic crystalline elements in the front group 412 ispreferably substantially similar in magnitude and variation with pupiland field position to the net retardance produced by the rear group 414.The location of the polarization rotator 410 is so chosen such that theretardance introduced by the second group 414 may compensate of theretardance produced by intrinsic birefringence.

In addition to the 90° polarization rotator 410, a −90° polarizationrotator 420 is added to the lens 400 in between the object plane 404 andthe first lens element L1 to balance the circular retardance produced bythe 90° rotator 410. The addition of this second polarization converter420 in the lens model is a computational aid for calculating thedifferences in retardance from 90 degrees. With the second rotator, thedesigner may reduce the magnitude of the retardance to zero. Without thesecond rotator, the designer would monitor the magnitude and shape ofthe retardance and adjust the design, for example, so that the magnitudeand shape of the retardance are substantially constant across the pupil.This latter merit function would have twice as many terms and would takelonger to compute and optimize.

To minimize variation in retardance with field, each optical elementL1-L28B is oriented with its [110] crystal lattice directionsubstantially parallel with the system optical axis 402, such that thepeak birefringence node is along the optical axis 402 and the outer peakbirefringence lobes are at an angle of 60° with respect to the opticalaxis 402.

Furthermore, in the lens 400 illustrated in FIG. 37, two of the lenselements L27A and L27B, which were combined in one element L27 in theexemplary lens system of FIG. 32 have each been split into two that havethe same total thickness and power. Also, two of the lens elements L28Aand L28B, which were combined in one element L28 in the lens system ofFIG. 32 have each been split into two that have the same total thicknessand power. These lenses are marked by cross-hatching in FIGS. 32 and 37.The thicknesses for the sets of segments L27A, L27B and L28A, L28B aswell as the curvature of the respective buried surfaces 418 and 422between them is optimized to minimize the net system retardance. Theseadditional degrees of freedom are shown to improve the achievableretardance compensation without requiring redesign of the lens 400.

A toroidal surface 424 is also provided on one of the optical elementsL19, identified by cross-hatching, to compensate residual astigmatismdue to variations in average index of refraction. Another effectproduced by intrinsic birefringence in the cubic crystal lattice isvariation of the average index of refraction as a function of ray anglethrough the crystal. In addition to compensating for retardance errorsresulting from intrinsic birefringence, residual wavefront aberrationsresulting from the variations in average index of refraction can becorrected. If uncorrected, this variation in average index of refractionmay produce astigmatism in the wavefront. As such, the optical designincludes this toroidal surface 424 to compensate for the effects ofvariations in average index of refraction. This toroidal surface 424 hasa radii of curvature of −218.60371 mm along the local Y direction and−218.603789 mm along the local X direction.

These techniques may be applied to allow the retardance contributions ofthe elements L1-L24 preceding the 90° polarization rotator 410 tosubstantially balance the net retardance of the elements L25-L28Bfollowing the 90° rotator 410 and provide an overall wavefrontcorrection that is acceptable for high numerical aperture lithographysystems.

Further improvement in retardance compensation can be achieved byoptimizing the relative rotations of the lens elements L1-L28B about theoptical axis 402. The process of rotating one or more of the opticalelement L1-L28B about the optical axis 402 is referred to as clockingand is discussed in U.S. patent application Ser. No. 10/071,375, filedFeb. 7, 2002, entitled “Correction of Birefringence in Cubic CrystallineOptical Systems” now U.S. Pat. No. 6,683,710, which is incorporatedherein in its entirety by

reference. This form of rotation of the optical element L1-L28B itselfmay be employed to reduce net retardance, as the birefringence axesacross the pupil plane are reoriented so as to at least partially cancelout the retardance introduced by the different elements L1-L28.

In one embodiment, the lens elements L1-L28B have clockings given inTable 9. The clocking of each element is given relative to anorientation that produces peak birefringence along the optical axis 402and that is oriented with the retardance axis substantially parallel tothe X axis (horizontal, in the direction perpendicular to the specifiedfield of view).

TABLE 9 Element Element Clocking (degrees) L1 137.42 L2 −177.91 L3−137.96 L4 −21.23 L5 49.30 L6 112.63 L7 −71.76 L8 23.92 L9 49.96 L1056.81 L11 132.09 L12 −154.83 L13 −17.35 L14 96.91 L15 146.55 L16 148.96L17 −41.95 L18 −21.28 L19 100.60 L19, Surface 2 (Toroid) 169.00 L20178.67 L21 −124.36 L22 −44.90 L23 134.50 L24 137.49 L25 −124.00 L2643.52 L27A 81.40 L27B 160.62 L28A −49.38 L28B 27.57

Accordingly, a given lens prescription can be improved by splitting atleast one of the individual lens element (L27 or L28 in this case) into(i.e. replacing it with), two or more sub-elements L27A, L27B, and L28A,L28B. The sub-elements L27A, L27B, and L28A, L28B each include the sameoverall radius of curvature and include the same thickness so that theoverall optical qualities of the original lens prescription are notadversely affected. For each individual element L27, L28 being replaced,the sub-elements L27A, L27B, and L28A, L28B are oriented to reduce netsystem retardance relative to the retardance correction achievable usingthe individual lens element L27, L28 which they combine to replace. Eachof the sub-elements L27A, L27B, and L28A, L28B may be aligned with thesame crystal axis along the optical axis 402, and the sub-elements L27A,L27B, and L28A, L28B may be clocked relative to each other. For example,each of the sub-elements may be a [110] or [100] optical element. Inanother exemplary embodiment, the sub-elements may include differentcrystal axes aligned along the optical axis, for example, a [100]optical element and a [110] optical element. Compensating [110] elementswith [100] elements is disclosed in U.S. patent application Ser. No.10/071,375, filed Feb. 7, 2002, entitled “Correction of Birefringence inCubic Crystalline Optical Systems” now U.S. Pat. No. 6,683,710, which ishereby incorporated herein in its entirety by reference.

In one embodiment the optical element L27 of FIG. 32 is split into two[110] optical sub-components L27A and L27B of FIG. 37 and opticalelement L28 of FIG. 32 is split into two [110] optical sub-componentsL28A and L28B of FIG. 37 to provide fine adjustment of the compensation.The combined thickness of lens sub-elements L28A and L28B of FIG. 37 issubstantially the same as the thickness of lens element L28 of FIG. 32.The thicknesses and radii of curvature of buried surfaces 418 and 422provide control over the retardance aberrations at the center and edgeof the pupil. Table 10 lists the clocking, radii of curvature andthicknesses of the optical sub-elements produced by splitting componentsL27 and L28.

TABLE 10 Element Clocking Front Radius of Back Radius of ThicknessElement (degrees) Curvature (mm) Curvature (mm) (mm) L27A 81.40−10831.21505 348.95732 29.677503 L27B 160.62 348.95732 322.3940720.322497 L28A −49.38 399.72415 58.37955 24.114117 L28B 27.57 58.37955−1901.87993 25.885883

FIGS. 38A and 38B are graphical representations that depict theretardance across the system exit pupil for optical elements L1-L24 inthe front group 412 of lens in the system 400, between the −90° and 90°rotators 410 and 420. The retardance is caused by the intrinsicbirefringence and anti-reflection coatings. As previously shown in Table6, the contribution due the coatings is relatively small; thus, the bulkof the retardance aberration is due to the intrinsic birefringence. FIG.38A shows net retardance at the center field point and FIG. 38B showsnet retardance at the edge field point. It can also be seen in FIGS. 38Aand 38B that the retardance is substantially similar for the center andedge field points, showing that alignment of each element L1-L24 withits [110] crystal lattice direction along the optical axis 402 resultsin low sensitivity to angle of incidence variations resulting fromchanges in field height.

FIGS. 39A and 39B are graphical representations that depict theretardance across the system exit pupil for optical elements L25-L28B inthe rear group 414 of the system 400, between the 90° rotator 410 andthe image plane 406. FIG. 39A shows net retardance at the center fieldpoint and FIG. 29B shows net retardance at the edge field point.

Comparing FIGS. 38A, 39A, 38B, and 39B, the net retardance from thefront group 412 of the system 400 is substantially similar to the netretardance from the rear group 414 of the system 400 across the pupiland at center and edge field points. Thus, because the 90° rotator 410rotates each constituent polarization state by 90°, the retardanceintroduced by the rear group 414 of the 400 system will compensate theretardance introduced by the front group 412 of the system 400.

FIGS. 40A and 40B are graphical representations that depict the netretardance across the system exit pupil at central and edge field pointsdue to intrinsic birefringence of all elements L1-L28B, including the90° and −90° rotators 410 and 420. As shown, the net retardance has beensignificantly reduced at both fields compared with the retardance forall [110] elements without rotators 410 and 420 shown in FIGS. 34A and34B.

The RMS and maximum retardance over the exit pupil are listed in Table11 below for relative field heights of 0, 0.7, and 1.0. These includethe effects of intrinsic birefringence and the single layeranti-reflection coatings used in the model. A relative field height of0.0 corresponds to the center field point, for which the results aregraphically in FIG. 40A, and a relative field height of 1.0 correspondsto the edge field point, the retardance contributions of which is showngraphically in FIG. 40B. The RMS retardance ranges from 0.0033 to 0.0065waves at λ_(o)=193.3 nm.

TABLE 11 Retardance (waves at λ_(o) = 193.3 nm) Relative Field HeightRMS Maximum 0.0 0.0033 0.0198 0.7 0.0044 0.0228 1.0 0.0065 0.0383

The retardance using all [110] elements without polarization converters410 and 420 was shown in FIGS. 34A and 34B. With the two rotators 410and 420, optimized clocking of the elements L1-L28B, and splitting oftwo elements L27 and L28, the maximum retardance was reduced from 2.12waves to 0.0198 waves at λ=193.3 nm for the axial field (107× reduction)and a reduction in maximum retardance from 2.14 waves to 0.0383 waves atthe extreme field (56× reduction).

The RMS and peak-to-valley wavefront error are listed in Table 12 forthe compensated design that includes the effects of intrinsicbirefringence. The wavefront errors are given for relative field heightsof 0, 0.7, and 1.0 in the Y direction, and are listed for two orthogonalpolarization components. The X component represents the wavefront errorfor an input polarization in the X direction assuming a linear polarizeralong the X direction at the system exit pupil. The Y componentrepresents the wavefront error for an input polarization in the Ydirection assuming a linear polarizer along the Y direction at the exitpupil. An RMS wavefront error that varies from 0.010 to 0.014 wavesacross the field is achieved. The peak-to-valley wavefront error isreduced by a factor ranging from approximately 8 to 22, in exemplarylenses in which all elements are [110], [100], or [111] optical elementsoriented substantially identically. Thus, this embodiment demonstratesthat intrinsic birefringence effects can be reduced to a levelacceptable for high numerical aperture lithography.

TABLE 12 RMS Wavefront Error Peak-to-Valley (waves at Wavefront Errorλ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) Relative Field X Y X YHeight Component Component Component Component 0.0 0.010 0.010 0.0560.050 0.7 0.011 0.013 0.079 0.077 1.0 0.011 0.014 0.097 0.088

In FIGS. 41A, 41B, 41C, and 41D, wavefront errors are plotted at thesystem exit pupil as contour maps. FIGS. 41A and 41B show contour plotsof the residual wavefront error for the lens 400 depicted in FIG. 37corresponding to an input polarization in the X direction, perpendicularto the field height, used with an exit pupil analyzer in the X directionfor the central and extreme field points, respectively. For the centralfield point, the maximum peak-to-valley optical path difference is 0.056waves at a wavelength of 193.3 nanometers, and at the extreme field, themaximum peak-to-valley optical path difference is 0.097 waves. FIGS. 41Cand 41D show contour plots of the residual wavefront error for the lens400 depicted in FIG. 37 corresponding to an input polarization in the Ydirection, parallel to the field height, used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the central field point, the maximum peak-to-valleyoptical path difference is 0.050 waves at a wavelength of 193.3nanometers, and at the extreme field, the maximum peak-to-valley opticalpath difference is 0.088 waves.

The centroid distortion for the compensated design with intrinsicbirefringence, calculated based on the point spread function, and thetelecentricity error in the Y direction are listed at relative fieldheights of 0, 0.7, and 1.0 in Table 13 below. As shown, there was anincrease in maximum X distortion of about −0.3 nm and an increase inmaximum Y distortion of 6.7 nm, compared with the distortion for thenominal design without intrinsic birefringence given in Table 8.Adjustment of some of the radii of curvature of the design allows thesechanges in distortion to be compensated and reduced. Changes intelecentricity error from the nominal design are negligible.

TABLE 13 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 −0.28 10.63 0.11 1.0 0.22 17.39 0.51

Although lens 400 depicted in FIG. 37 included thirty refractive opticalelements L1-L28B, other embodiments may comprise more or less opticalelements which may be reflective, diffractive, and/or refractive.Similarly, the optical elements may have spherical or aspheric surfaces,may be powered or unpowered, may be off-axis or on axis. Other opticallytransmissive elements may include diffractive and holographic opticalelements, plates, filters, mirrors, beamsplitters, windows, to name afew. Additionally, all the optical elements need not comprise the samematerial. These optical elements may be crystalline or non-crystallinesuch as amorphous glasses. In the case where at least some of theelements are crystalline, they do not need to all be the same crystalorientation. For example, various combinations of cubic crystal opticalelement having a [111], [100], and/or [110] crystal direction may besuitable employed.

Example 5

A catadioptric optical system 500, which has both refractive andreflective optical elements L1-L19 and M1-M3, such as depicted in FIG.42, can be used as a projection lens for photolithography. Such anexemplary lens 500 is disclosed in U.S. Pat. No. 6,195,213 by Y. Ohmura,the contents of which are hereby incorporated herein by reference. Thissystem 500 includes an object field 502, and image field 504, andmultiple optical axes. The system 500 is separated into two arms 506 and508, the first arm 506 including a portion of the lens elements, L1-L8,as well as the first mirror M1 substantially aligned along a firstoptical axis. The second arm 508 includes the remainder of the lenselements L9-L19 substantially aligned along a second optical axis. Thetwo arms are optically connected via planar folding mirrors M2 and M3.The system 500 advantageously operates at a central wavelength ofλ_(o)=193.3 nm and at a numerical aperture of 0.75 and provides 4×reduction. The image field 504 is 34.25 mm in diameter, but the foldmirror M2 at an intermediate image partially obscures the beam, givingan image field 504 that extends from a height of 5 mm to 17.125 mm withrespect to second optical axis in the plane of the folded beam. All lenselements L1-L19 are constructed from fused silica in the design shown byY. Ohmura in U.S. Pat. No. 6,195,213, but may comprise cubic crystalmaterial and in particular cubic crystal calcium fluoride. For thepurpose of calculation, the results of which are provided below, eachtransmissive optical component is assumed to have an intrinsicbirefringence of −12×10⁻⁷. According to other exemplary embodiments,however, some of the lens elements L1-L19 may be formed of non-cubiccrystalline material or additional lens elements or other opticallytransmissive components formed of non-cubic crystalline material may beused. Various suitable non-cubic crystalline materials such as dry fusedsilica may be employed for operation in the ultraviolet.

The RMS and maximum retardance and diattenuation over the exit pupil arelisted in Table 14 below for the nominal design without intrinsicbirefringence effects included for image field heights of 5, 11, and17.125 mm. The retardance and diattenuation result from the single-layeranti-reflection coatings used in the model. The retardance variesradially outward and is largest in magnitude at the edge of the pupil.The retardance due only to the anti-reflective coating is relativelysmall.

TABLE 14 Retardance (waves Image Field at λ_(o) = 193.3 nm)Diattenuation Height (mm) RMS Maximum RMS Maximum 5 0.0039 0.0146 0.00540.0225 11 0.0039 0.0156 0.0054 0.0240 17.125 0.0040 0.0176 0.0056 0.0268

When the effects of intrinsic birefringence associated with the cubiccrystalline lens material are taken into account, system performancedegrades significantly. FIGS. 43A and 43B are graphical illustrationsshowing the net retardance across the system exit pupil for image fieldpoints of 5 and 17.125 mm, respectively, according to the exemplaryembodiment in which all refractive lens elements L1-L19, shown in FIG.42, have crystal axes that are identically aligned in three dimensions,with the elements L1-L19 having their [110] crystal axis along therespective optical axis for the particular lens elements L1-L19. FIGS.43A and 43B include the effects of intrinsic birefringence. In theretardance pupil maps given in FIGS. 43A and 43B, and in others tofollow in which the net retardance exceeds a magnitude of 0.5 waves, theretardance is plotted “modulo 1 wave.” It can therefore be seen that theretardance orientation rotates by 90 degrees at one-half-wave intervals,i.e., the effect of a 0.75 wave retarder at 0 degrees is the same as a0.25 wave retarder at 90 degrees. Thus, the peak retardance due tointrinsic birefringence in this exemplary arrangement is approximately0.8 waves at a wavelength of 193.3 nanometers at image heights of 5 mmand 17.125 mm.

FIGS. 44A and 44B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem 500 shown in FIG. 42. In FIGS. 44A and 44B, the net retardanceacross the system exit pupil, including the effects of intrinsicbirefringence, is depicted for field points at the center and edge ofthe field with all elements L1-L19 having crystal axes alignedidentically in three dimensions, with their [100] crystal axes along therespective optical axis for the particular lens element L1-L19. Again,the retardance orientation rotates by 90 degrees at one-half-waveintervals; thus, the peak retardance due to intrinsic birefringence isapproximately 1.4 waves at a wavelength of 193.3 nanometers at an imageheight of 5 mm and 1.2 waves at the extreme field, if the retardancewere not plotted “modulo 1 wave”

FIGS. 45A and 45B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem 500 shown in FIG. 42. In FIGS. 45A and 45B, the net retardanceacross the system exit pupil is depicted for field points at the centerand edge of the field with all elements L1-L19 having crystal axesaligned identically in three dimensions, for [111] optical elementshaving the [111] crystal direction substantially parallel to the opticalaxis for the particular lens element L1-L19. The peak retardance due tointrinsic birefringence is approximately 0.5 waves at a wavelength of193.3 nanometers at image heights of 5 mm and 17.125 mm.

These cubic crystal elements are described as [111] optical elementsbased on the direction of the crystal axis at the optical axis. Sincemany of the rays in the beam propagating through the optical system areclustered around the optical axis, many of the rays will be nearlyparallel to the crystal axis. Because of the symmetry of the lensdesign, the element optical axis corresponds to the system optical axis.

Each of three preceding examples, as illustrated in FIGS. 43A-45B, showsthat the intrinsic birefringence produces large retardance aberrationsand consequently large wavefront aberrations, when each of the crystalelements are oriented identically with respect to the respective opticalaxis. Without compensation, this aberration strongly exceeds theallowable wavefront error for high precision photolithography.

To correct this wavefront aberration, two polarization rotators 510 and520 are added to the optical system 500 to reduce the retardanceproduced by the intrinsic birefringence of the refractive opticalelements L1-L19 as shown in FIG. 46. All these refractive opticalelements L1-L19 are oriented in this embodiment with identicalthree-dimensional crystal lattice directions, and are [111] elements.The [111] crystal lattice direction for each element L1-19 is along thesystem optical axis.

Choosing as many cubic crystalline elements with their respective [111]crystal lattice directions along the system optical axis is particularlyadvantageous for construction of optical systems. High purity cubiccrystals, such as CaF₂ crystals for VUV optical lithography systems,naturally cleave along the (111) plane, and single crystals are moreeasily grown along the [111] direction. As a result, lens blanks forconstruction of [111] optical elements are typically less expensive andmore easily available than lens blanks oriented along other latticedirections. Furthermore, the stress optic coefficient is lower along the[111] direction than along the [100] or [110] directions, reducing imagedegradation resulting from mount-induced stress. Accordingly, an exampleof this preferred arrangement is presented, in which all powered cubiccrystalline elements comprise [111] refractive optical element areoriented with their respective [111] crystal axes along the opticalaxis.

Alternate embodiments, however, may include optical componentscomprising other cubic crystal material having their crystal axesoriented differently. The lens may for example include one or more [100]and/or [110] optical elements with the respective [100] and [110]lattice directions substantially parallel to the optical axis 540. Suchlens elements, appropriately clocked, can be included to compensate forretardance produced, for example, by [111] optical elements as discussedin U.S. patent application Ser. No. 10/071,375, filed Feb. 7, 2002,entitled. “Correction of Birefringence in Cubic Crystalline OpticalSystems” now U.S. Pat. No. 6,683,710, which is incorporated herein inits entirety by reference. Preferably, however, the majority or morepreferably a substantial majority of the cubic crystal optical elementsthrough which the beam passes in-the optical system comprise [111]optical elements. For example, 70, 80, 90, percent or more of the cubiccrystalline optical elements in the path of the beam in the opticalsystem 500 preferably comprise [111] cubic crystal optics. Thesepercentages may apply to just the cubic crystal lens elements or maymany include both lens elements as well as other optical elements, suchas, e.g., waveplates. Alternatively, the percentage, by weight, of [111]cubic crystal of all the cubic crystal material in the optical path ofthe lens 500 is preferably more than 50%, more preferably at least about80% and most preferably 90% or more. This percentage may include onlypowered refractive optical elements as well as powered and non-poweredoptical elements such as waveplates, windows, etc. For example, 90% ofnet weight of the cubic crystal lens may comprise cubic crystal having a[111] axis oriented along the optic axis. In another example, 80% of thenet weight of the cubic crystal optics, including the waveplates thatform the polarization rotators, may be [111] cubic crystal, with the[111] axis parallel to the optic axis. The cost of materials for such asystem is significantly reduced in comparison with optical systems thatemploy more [110] or [100] crystal material. The use of the polarizationconverter in reducing the retardance aberration enables such a largepercentage by weight of [111] crystal material to be used without undulydegrading the optical performance of the system. In other embodiments,some of the lens elements or other optical elements may be formed ofnon-cubic crystalline material or additional lens and/or opticalelements formed of non-cubic crystalline material may be used. Varioussuitable non-cubic crystalline materials such as dry fused silica mayoffer other lower cost alternatives.

As discussed above, however, all the refractive optical elements L1-L19in the lens 500 shown in FIG. 46, comprise [111] cubic crystal with the[111] crystal direction parallel to the optical axis. The 90° rotator510 is positioned between the sixteenth and seventeenth lens elementsL16 and L17 to reduce the net system retardance. The −90° rotator 520 islocated between the object plane 502 and the first element L1. Forpurposes of calculations, the rotators 510 and 520 are assumed to beideal polarization rotators, such that each constituent polarizationstate is rotated by exactly 90 or −90°. Additionally, the polarizationrotators 510 and 520 are assumed to have zero thickness. As discussedabove, the lens prescription may be adjusted and optimized for finitethickness rotators 310 and 320 as well.

As discussed above, the 90° polarization rotator 510 splits the lens 500into two parts, a front and rear section of the lens 500. The locationof the rotator 510 is chosen such that the net retardance produced bythe cubic crystalline elements L1-L16 in the front part of the system500 is similar in magnitude and orientation as a function of field andpupil position to the net retardance produced by the cubic crystallineelements L17-L19B in the rear part of the system 500. The rotator 510allows the retardance contributions of the individual elements L1-L19Bto be balanced to provide wavefront correction and reduce the netretardance produced by the intrinsic birefringence to a level that isacceptable for the particular application, e.g., for high numericalaperture lithography systems.

With this design, the system will have a uniform circular retardance of90 degrees and the input will experience reduced wavefront aberrations,although the polarization state will be rotated by 90 degrees betweenthe object (reticle) and image (wafer) planes, because of theintroduction of 90 degrees of circular retardance. In order to evaluatethe magnitude of the deviation of the retardance from 90 degrees, aperfect circular retarder 520 of −90 degrees (i.e., a −90 degreerotator) has been inserted between the object and first lens element.The second rotator cancels out the nearly constant 90 degrees ofcircular retardance introduced by the first rotator, leaving only thesmall residual retardance aberrations. This second rotator 520 is usedin this example as a computational aid and may or may not be included ina particular optical system, unless the input and output polarizationsneed to be identical (which is not usually the case). It is much easierto visualize small retardance variation with the large constant 90degree circular retardance removed. The second rotator also simplifiesthe construction of the optimization merit function as it only has toinclude the magnitude of the retardance and not the shape of theretardance. Insertion of the second rotator 520 into the lens model alsofacilitates optimization of the system 500 by allowing the designer toreduce the magnitude of the deviation of the retardance from 90 degrees.However, an additional rotator 520 would introduce further complexityand cost to the optical system 500.

The optical axis in each of the arms 506 and 508 are substantially alongthe Z direction, the field is oriented in the Y direction, and aright-handed coordinate system is used; thus, a 90° rotation about theoptical axis represent a rotation of the X axis towards the Y axis. Theorder of the rotators 510 and 520 may be switched without changing theperformance, such that the 90° rotator 510 is used in object space, andthe −90° rotator 520 is used between the sixteenth and seventeenth lensL16 and L17. Also, the rotator 520 in object space may, in principle, bealternatively used in image space (between last element L19B and imageplane 504).

As discussed above, the lens elements L1-L19B in an optical system 500can be rotated about the optical axis, herein termed clocking, to reduceretardance. The birefringence contributions across the lens pupil arerepositioned and potentially reoriented such that the birefringence oftwo or more lenses compensate and offset each other. In one preferredembodiment, for example, the lens elements L1-L19B in the lens 500 ofFIG. 46 have clockings given in Table 15. The clocking of each elementL1-L19B is given relative to an orientation that produces peakbirefringence along the optical axis that is oriented with theretardance axis substantially parallel to the X-axis (horizontal, in thedirection perpendicular to the specified field of view).

TABLE 15 Element Element Clocking (degrees)  1 325.71  2 7.06  3 143.41 4 76.83  5 230.04  6 113.19  7 −2.21  8 56.48  9 208.29 10 170.00 11−9.41 12 379.75 13 −14.21 14 95.43 15 198.23 16 140.64 17 236.41 18168.37 19 (19A) 178.09 20 (19B) 4.18

In addition, in one preferred embodiment, the last element L19 in FIG.42 has been replaced by, i.e., split into, two sub-elements, L19A andL19B of FIG. 46 with buried surface 512 between them. These lenselements L19, L19A, and L19B, are cross-hatched in FIGS. 42 and 46. Thesub-elements L19A and L19B each include the same overall outer radii ofcurvature. The sub-elements L19A and L19B are oriented (clocked) toreduce net system retardance relative to the retardance correctionachievable using the element L19 which they combine to replace. Here,each of the sub-elements L19A and L19B has its [111] crystal axisparallel to the system optical axis, but the other crystal axes of thetwo elements L19A and L19B are rotated about the optical axis withrespect to one another. The radius of curvature of buried surface 512and the thicknesses of sub-elements L19A and L19B were optimized tominimize net retardance.

Here, the combined thickness of sub-elements L19A and L19B was allowedto vary relative to the thickness of element L19 in FIG. 42. The centerthickness of element L19 was initially 65 mm, but the combined thicknessof L19A and L19B was reduced to 45.5820 mm. Also, the thickness ofelement L1 in FIG. 42 was reduced in thickness from 59.9763 mm to41.2024 mm. These changes to the nominal lens prescription introduceadditional wavefront, not retardance aberrations, that may be correctedby means which are commonly practiced by those skilled in the art. Thelens design has not been further modified to correct for the additionalwavefront errors, so as to illustrate the correction of the retardanceaberrations. Additionally, the current embodiment has not beenreoptimized to correct for the changes in element thicknesses;therefore, this example shows reduction of net system retardance to anacceptable level for lithographic imaging.

Table 16 lists the radii of curvature and thicknesses opticalsub-elements L19A and L19B produced by splitting component L19 in thedesign shown in FIG. 42.

TABLE 16 Element Clocking Front Radius of Back Radius of ThicknessElement (degrees) Curvature (mm) Curvature (mm) (mm) 19 178.09−316.06140 −218.78841 −26.391552 20 364.18 −218.78841 12272.48200−19.190442

FIGS. 47A and 47B are graphical representations that depict theretardance across the system exit pupil for optical elements L1-L16 inthe front part of the system 500, between the −90° rotator 520 and the90 rotator 510. FIG. 47A shows net retardance at an image height of 5 mmand FIG. 47B shows net retardance at an image height of 17.125 mm.

FIGS. 48A and 48B are graphical representations that depict theretardance across the system exit pupil for optical elements L17-L19B inthe rear part of the system 500, between the 90° rotator 510 and theimage plane 504. FIG. 48A shows net retardance at an image height of 5mm and FIG. 48B shows net retardance at an image height of 17.125 mm.

Comparing FIGS. 47A, 48A, 47B, and 48B, the net retardance from thefront part of the system 500 is similar to the net retardance from therear part of the system 500 across the pupil and at image heights of 5mm and 17.125 mm. Thus, because the 90° rotator 510 rotates eachconstituent polarization state by 90°, the retardance of the rear partof the system 500 will compensate the retardance of the front part ofthe system 500.

FIGS. 49A and 49B are graphical representations that depict the netretardance across the system exit pupil at central and edge field pointsdue to intrinsic birefringence of all elements L1-L19B, 510, 520,including the 90° and −90° rotators 510, 520. As shown, the netretardance has been significantly reduced at both fields compared withthe retardance for all [111] elements without rotators 510 and 520 shownin FIGS. 45A and 45B. Thus, substantial retardance correction for asystem 500 comprising all [111] optical elements L1-L19, is possible, byusing a polarization converter that transforms the polarization of thelight within the optical system 500 into a polarization state rotated by90°. In particular, the intrinsic birefringence effects and systemretardance of this catadioptric optical system 500 are significantlyreduced to levels acceptable for high numerical aperture lithography.

The RMS and maximum retardance over the exit pupil are listed in Table17 below for image field heights of 5 mm, 11 mm, and 17.125 mm. Theseinclude the effects of intrinsic birefringence and the single layeranti-reflection coatings used in the model. The RMS retardance rangesfrom 0.0037 to 0.0059 waves at λ_(o)=193.3 nm.

TABLE 17 Retardance (waves at λ_(o) = 193.3 nm) Relative Field HeightRMS Maximum 0.0 0.0043 0.0244 0.7 0.0037 0.0206 1.0 0.0059 0.0314

This catadioptric lens 500 of FIG. 46 has twenty (20) lens elementsL1-L19B, six of which are used in double pass (L3-L8), each comprising[111] cubic crystal material with the [111] crystal axis parallel to theoptical axis passing through the respective lens element. Thecatadiopric lens 500 further includes one powered mirror M1, and twofold mirrors M2, M3. The refractive optical elements L1-L19B areclocked, i.e., rotated about the optical axis passing therethrough toreduce retardance. The 90° polarization rotator 510, which divides theoptical system 500 into two parts having similar net birefringence,causes the retardance introduced by the two parts to compensate for andoffset each other. The −90° polarization rotator 520 in object spacecompensates for the constant retardance produced by the 90° rotator 510.The element L19 in FIG. 42 closest to the image plane is split into two[111] components L19A and L19B with different relative clockings, andthe thicknesses of the components and radius of curvature of the buriedsurface 412 are optimized to minimize net retardance. The peak-to-valleyretardance can thereby be improved by a factor ranging from 15.6× to18.9×.

Other compensation techniques maybe applied to reduce retardance. In anexemplary embodiment, one or more stress birefringent elements, waveplates, or combinations thereof may additionally be used to providecompensation and correct for residual birefringence variation andconstant residual retardance which remains in the catadioptric systemafter the above-described system corrections have been made. Techniquesdisclosed in U.S. patent application Ser. No. 10/071,375, filed Feb. 7,2002, entitled “Correction of Birefringence in Cubic Crystalline OpticalSystems” now U.S. Pat. No. 6,683,710, which is incorporated herein inits entirety by reference may also be employed. One of these techniquesincludes, for example, adding [100] optical elements that areappropriately rotated with respect to the optical axis to providecompensation.

In addition, stress may be applied to a reflective element such asmirror surfaces M1, M2, or M3 to alter the base radius of curvature inorthogonal directions. This stress may correct for residual astigmatismin the catadioptric optical system. The use of at least one opticalelement whose base radius of curvature differs in orthogonal directionsmay additionally or alternatively be used to compensate for residualastigmatism. For example, residual astigmatism due to variations in theaverage index of refraction from [110] optical elements can be counteredby varying the base radius of curvature of at least one surface of anoptical element, in orthogonal directions. Residual trefoil wavefrontaberrations due to variations in the average index of refraction in[111] optical elements can also be compensated by varying the shape,e.g., radius of curvature, of at least one surface of an optical elementwith an azimuthal angular dependence of 30 to reduce this aberration. Ifthe optical axis is along the z-axis, the azimuthal angle, θ, is in thex-y plane and measured from the x-axis. Quadrafoil wavefront aberrationsdue to variations in the average index of refraction from [100] crystalscan likewise be countered. Compensation maybe achieved by varying theshape of at least one optical element with an azimuthal angulardependence of 4θ.

Another example of a catadioptric systems that include beam splitters orwave plates, is described in U.S. Pat. No. 6,081,382 by Ohmura, et al,which is incorporated herein in its entirety by reference. Thepolarization aberrations in this system also may be corrected, forexample, with the addition of at least one polarization rotator todivide the optical system into multiple groups, such as two groups withsimilar net retardance. In addition, relative clocking of the opticalelements, the inclusion of various combinations of [111], [110], and[100] optical elements, stress-induced birefringent elements withradially varying stress, stress induced birefringent elements withstress varying along axes perpendicular to the optical axis, theoptimization of lens element thicknesses, spacings, radii of curvatureand aspheric coefficients can be used to decrease the affect ofaberrations that degrade optical performance. Similarly, residualastigmatism, trefoil aberration, and quadrafoil aberration due tovariations in the average index of refraction in [110], [111], and [100]cubic crystalline optical elements, can be reduced through the use of atleast one optical element whose base radius of curvature varies as 2θ,3θ, and 4θ.

Some of the preceding examples are based on lens prescriptions publishedin the prior art. These examples are intended to be exemplary only andthe principles applied with reference to these examples can be extendedto any of various other lens designs. However, application of techniquesdescribed above for reducing retardance aberration are of particularinterest for high numerical aperture optical systems forphotolithography at an exposure wavelength near 157 nm, such as thatproduced by an F₂ excimer laser. Because many of the available opticalsystems described in the art include lower numerical apertures andoperate at longer wavelengths such as 193 nm, the techniques areillustrated by application to exemplary known optical systems designedfor an exposure wavelength near 193 nm, corresponding to the wavelengthproduced by an ArF excimer laser, commonly used in photolithography. Itshould be understood, however, that these principles and techniquesapply equally to high numerical aperture systems and systems operatingat 157 nm.

Furthermore to estimate the effects of intrinsic birefringence in highnumerical aperture lenses designed for a central wavelength of 157 nm,in which the refractive elements are primarily constructed from calciumfluoride, each element is assumed to have a peak intrinsic birefringenceof (n_(e)-n_(o))=−12×10⁻⁷, which is roughly equivalent to the measuredpeak intrinsic birefringence in calcium fluoride at a wavelength of 157nm. In other embodiments, however, one or more of the optical elementsmay be constructed from other materials such as barium fluoride, lithiumfluoride, strontium fluoride, and fused silica. In addition, opticalelements comprising material exhibiting positive birefringence can beincluded to compensate for the effects of optical elements comprisingmaterial exhibiting negative birefringence.

In this manner, the method for compensation of intrinsic birefringencein similar high numerical aperture lenses designed for 157 nm may bedemonstrated using known exemplary lens descriptions designed for acentral wavelength of 193 nm as starting points. The change in centralwavelength may result in a change in refractive index of the refractivecomponents and may warrant the use of fluoride materials such as calciumfluoride, but the types of elements used and distributions of ray anglesfor a given numerical aperture are similar enough to allow a lensdesigned for a central wavelength of 193 nm to be used to demonstratethe innovative techniques for mitigating the effects of intrinsicbirefringence in high numerical aperture lenses, at a central wavelengthof 157 nm. The design techniques presented above, however, may beemployed for reducing polarization aberration in optical systemsoperating at other wavelengths.

In calculating the performance of some of optical systems in theexamples discussed above, the refractive surfaces are assumed to have ahypothetical, single layer anti-reflection coating with an index ofrefraction equal to the square root of the element index of refractionand with an optical thickness of a quarter wave at a wavelength of 193.3nm. The indices of refraction for calcium fluoride and fused silica usedin some of the examples described above are assumed to be 1.501455 and1.560326, respectively, at a wavelength of 193.3 nm. Different coatingswill introduce different retardance and phase aberrations and mayrequire slightly different compensation. It should be understood,however, that the method demonstrated for the single hypotheticalcoating is applicable to systems with various other physical coatings orno coating at all.

The preceding examples are intended to be illustrative, not restrictive.Furthermore, it is intended that the various exemplary techniques forcountering the effects of intrinsic birefringence, including retardanceaberrations and wavefront aberrations produced by variations in averageindex of refraction may also be applied to the other embodiments. Moregenerally, these basic principles used to compensate for polarizationaberrations such as retardation and diattenuation can be extended to atleast partially correct for these effects in various other opticalsystems. The principles apply both to refractive and catadioptric lenssystems as well as other systems containing substantially opticallytransmissive material that imparts polarization aberrations on a beampropagating therethrough.

In other optical systems, the optical features of the optical componentsmay vary. For example, the individual thicknesses, radii of curvature,aspheric coefficients, and ray angles may differ significantly fromcomponent to component. Additionally the materials comprising theseoptical elements is not limited and may include non-cubic crystallineoptical elements as well as crystalline elements.

These principles may be used when designing new optical systems or toimprove a known lens prescription. In some of the examples above, thecorrected optical system is based on a given lens prescription, whichmay be maintained and the effects of intrinsic birefringence compensatedfor, using the techniques described above. Alternatively, retardationmay be reduced by splitting of one or more lens elements of the givenprescription, into two or more sub-elements. The location of the buriedsurface, its curvature and the thicknesses of the respectivesub-elements are degrees of freedom that may be adjusted to reduceaberration or provide other performance attributes. For example, theoptical power may be substantially evenly split into the sub-elements,which may or may not have same center thickness. The techniques anddesigns described above, however, may be advantageously applied tovarious other new lens prescriptions being designed.

Ray tracing software may be used to generate or revise the lensprescription including positioning of the individual lens elements, aswell as thicknesses, radii of curvature, aspheric coefficients, materialproperties, and the like. In one embodiment, the RMS retardance may becomputed over a pupil grid at each field point and used as the meritfunction for a damped least squares optimization using the commerciallyavailable ray tracing software, CODE V®, for example. A computer may beused to optimize the orientation and clocking of each of the elements inthe system. The thicknesses of the components, the spacings between thecomponents, and the radii of curvature and aspheric coefficients of thelens elements, may similarly be optimized to balance aberrations andreduce retardance across the field. One or more birefringent elements,wave plates, or combinations thereof, may additionally be used tocorrect for residual birefringence variation and constant residualretardance. Phase aberrations, such as astigmatism, trefoil aberration,and quadrafoil aberration, introduced by the average index variations in[110], [111], and [100] elements, respectively, may be compensated usingone or more surfaces with radii of curvature that vary as 2θ, 3θ, and4θ, respectively.

When cubic crystalline materials like calcium fluoride are used, asubstantial portion of these crystal elements preferably comprise lesserexpensive [111] cubic crystal with the [111] crystal lattice directionparallel to the optical axis. Although [100] and [110] elementsappropriately clocked can be added to compensate for the birefringenceintroduced by [111] elements, the cost of these [100] and [110] elementsis higher. The techniques described above advantageously permit thebirefringence of the [111] elements to be compensated for by other thelesser expensive [111] elements. Accordingly, the fraction of cubiccrystalline elements that comprise [111] crystal with the [111] crystallattice direction along the optical axis is preferably large, i.e., atleast 70-90%, by weight. Although the polarization rotator may be formedfrom various materials, it may comprise cubic crystal, such as [110],[100], or [111] cubic crystal elements. In some embodiments where thepolarization rotator comprises cubic crystal, preferably it comprisesmostly [111] cubic crystal, most preferably, all [111] cubic crystallinematerial. As discussed above, having many of the cubic crystal elementscomprise [111] material reduced the cost of the optics. Most preferably,a majority of the transmissive optical elements have an optical axisgenerally aligned with the [111] crystal lattice direction. In onepreferred embodiment, substantially all the optically transmissive cubiccrystal elements comprise this [111] crystal.

As discussed above, polarization rotation can be employed to correctpolarization aberrations other than retardance. Diattenuation, forexample, can also be reduced or substantially eliminated by inserting apolarization rotation device in an optical system. In one preferredembodiment, the diattenuation introduced by optical elements on oppositesides of the polarization rotator is matched or balanced. Accordingly, afirst polarization propagating through a first set of elements on afirst side of the rotator will be attenuated more than a secondorthogonal polarization. The two polarizations will be rotated and thepassed through a second set of elements on second opposite side of therotator. If the first and second sets of lens elements on the two sidesare matched, the second polarization will be attenuated by an amount ofattenuation experienced by the first polarization in the first set oflens elements. Accordingly, both the first and second polarizations willbe attenuated by substantially the same amount thereby reducing at leastin part the net diattenuation of the optical system. Other examples ofcorrection of polarization dependent aberrations and consideredpossible.

As mentioned above, the various exemplary cubic crystalline opticalsystems and methods for forming aberration-free patterns onsemiconductor substrates are particularly advantageous as feature sizesbecome increasingly smaller and approach the half wavelength of thelight used to produce the patterns. Such techniques find particularadvantage in high numerical aperture (NA) lens systems but the variousaspects these methods and innovations find application in opticalsystems having both relatively high and relatively low numericalapertures.

Although described in conjunction with photolithography tools used topattern substrates in the semiconductor industry, the techniques anddesigns discussed above will find use in a wide variety of applications,both imaging and non-imaging, in infrared, visible, and ultraviolet.Optical systems used for medical, military, scientific, manufacturing,communication, and other applications are considered possible candidatesfor benefiting from the innovations described herein.

Although described above in connection with particular embodiments ofthe present invention, it should be understood the descriptions of theembodiments are illustrative of the invention and are not intended to belimiting. Accordingly, various modifications and applications may occurto those skilled in the art without departing from the true spirit andscope of the invention. The scope of the invention is not to be limitedto the preferred embodiment described herein, rather, the scope of theinvention should be determined by reference to the following claims,along with the full scope of equivalents to which those claims arelegally entitled.

1-32. (canceled)
 33. An optical apparatus having an output comprising: aplurality of optical elements divided into first and second sections,said first and second sections having associated therewith polarizationaberrations originating from variation in optical properties of saidrespective sections with polarization, said polarization aberrationsaffecting said output of said optical apparatus, said polarizationaberrations associated with said first section being substantiallysimilar to said polarization aberrations associated with said secondsection; and polarization conversion optics disposed between said firstand second optical sections, said polarization conversion opticsconfigured to transform an input polarization into a orthogonal outputpolarization such that said polarization aberrations associated withsaid first section at least partially offset said polarizationaberrations associated with said second section and thereby reduce saideffects of polarization aberrations on said output of said opticalsystem.
 34. The optical apparatus of claim 33, wherein said plurality ofoptical elements comprise [111] cubic crystalline optical elementsaligned with their respective [111] lattice directions substantiallyparallel with an optical axis passing therethrough.
 35. The opticalapparatus of claim 34, wherein said first and second sections comprise[111] cubic crystalline calcium fluoride having a [111] latticedirection substantially parallel with an optical axis passingtherethrough.
 36. The optical apparatus of claim 33, wherein saidplurality of optical elements comprise [100] cubic crystalline opticalelements aligned with their respective [100] lattice directionssubstantially parallel with an optical axis passing therethrough. 37.The optical apparatus of claim 33, wherein said plurality of opticalelements comprise [110] cubic crystalline optical elements aligned withtheir respective [110] lattice directions substantially parallel with anoptical axis passing therethrough.
 38. The optical apparatus of claim33, wherein one or more optical elements comprise calcium fluorideoptical elements.
 39. The optical apparatus of claim 33, wherein saidpolarization aberration includes diattenuation, and said polarizationconversion optics are configured to reduce said diattenuation.
 40. Theoptical apparatus of claim 33, wherein said polarization aberrationincludes retardance, and said polarization conversion optics areconfigured to reduce said retardance.
 41. The optical apparatus of claim33, wherein said first and second sections have substantially similarretardance.
 42. The optical apparatus of claim 33, wherein said opticalconversion optic comprise an optical rotator.
 43. The optical apparatusof claim 33, further comprising a light source disposed with respect tothe plurality of optical elements to propagate light therethrough. 44.The optical system of claim 33, wherein said light source comprises anexcimer laser.
 45. The optical system of claim 33, wherein said opticalsystem is a non-imaging system.
 46. An optical imaging system forproducing an optical image, comprising: one or more powered opticalelements with polarization aberration that degrade said optical image;and a polarization rotation system configured to reduce saidcontributions of said polarization aberration to said degradation ofsaid optical image.
 47. The optical imaging system of claim 46, whereinsaid polarization aberration includes diattenuation, and saidpolarization rotation system is configured to reduce said diattenuation.48. The optical imaging system of claim 46, wherein said polarizationaberration includes retardance, and said polarization rotation system isconfigured to reduce said retardance.
 49. The optical imaging system ofclaim 46, wherein the polarization rotation system comprises a ±90(2n+1)degree rotator that rotates polarization by ±90(2n+1) degrees, where nis an integer.
 50. The optical imaging system of claim 46, wherein saidone or more powered optical elements are substantially opticallytransmissive to light having a wavelength less than or equal to about248 nanometers.
 51. The optical imaging system of claim 50, wherein saidone or more powered optical elements are substantially opticallytransmissive to light having a wavelength less than or equal to about193 nanometers.
 52. The optical imaging system of claim 51, wherein saidone or more powered optical elements are substantially opticallytransmissive to light having a wavelength less than or equal to about157 nanometers.
 53. The optical imaging system of claim 46, wherein saidone or more powered optical elements comprise cubic crystal.
 54. Theoptical imaging system of claim 53, wherein said one or more poweredoptical elements comprise material selected from the group consisting ofcalcium fluoride, barium fluoride, lithium fluoride, and strontiumfluoride.
 55. The optical imaging system of claim 46, wherein at leastof said one or more powered optical elements has a surface with anasymmetric variation in curvature.
 56. The optical imaging system ofclaim 55, wherein said surface with asymmetric variation in curvaturecomprises a toroidal surface.
 57. The optical imaging system of claim56, wherein said surface with asymmetric variation is positioned withinsaid optical imaging system to reduce astigmatism, trefoil aberration,or quadrafoil aberration of said optical system caused by variations inaverage index of refraction.
 58. The optical system of claim 46, furthercomprising an additional optical element comprising non-cubiccrystalline material and having a surface with an asymmetric variationin curvature.
 59. (canceled)
 60. An optical system comprising: a firstoptics section for receiving a beam of light having a polarization thatis propagating therethrough, said first optics section introducing phasedelay between orthogonal polarization states of said beam of light; asecond optics section outputting said beam of light, said second opticssection also introducing phase delay between said orthogonalpolarization states of said beam of light; and means for rotating thepolarization of said beam to reduce total phase delay between saidpolarization states of said beam of light output from said opticalsystem.
 61. The optical system of claim 60, wherein said phase delayassociated with said first optics section is substantially matched tosaid phase delay associated with said second optics section.